Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has created this Calculator and 400+ more calculators!
Shashwati Tidke
Vishwakarma Institute of Technology (VIT), Pune
Shashwati Tidke has verified this Calculator and 200+ more calculators!

11 Other formulas that you can solve using the same Inputs

angle between two lines given direction ratios of that two lines w.r.to x, y & z axis
Angle A= acos(((direction ratio 1 of line1*direction ratio 1 of line2)+(direction ratio 2 of line1*direction ratio 2 of line2)+(direction ratio 3 of line1*direction ratio 3 of line2))/(sqrt((direction ratio 1 of line1)^2+(direction ratio 2 of line1)^2+(direction ratio 3 of line1)^2))*(sqrt((direction ratio 1 of line2)^2+(direction ratio 2 of line2)^2+(direction ratio 3 of line2)^2))) GO
Direction cosine w.r.to x axis given direction ratio 1,2 & 3
Direction cosine with respect to z axis= (Direction ratio 1)/sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2) GO
Direction cosine w.r.to y axis given direction ratio 1,2 & 3
Direction cosine with respect to y axis= (Direction ratio 2)/sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2) GO
Direction cosine w.r.to z axis given direction ratio 1,2 & 3
Direction cosine with respect to z axis= (Direction ratio 3)/sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2) GO
x1 coordinate of end point of line given direction ratio and x2 coordinate of other end of that line
x1 coordinate in 3D space= Direction ratio 1-x2 coordinate in 3D space GO
x2 coordinate of end point of line given direction ratio and x1 coordinate of other end of that line
x2 coordinate in 3D space= Direction ratio 1-x1 coordinate in 3D space GO
y1 coordinate of end point of line given direction ratio and y2 coordinate of other end of that line
y1 coordinate in 3D space= Direction ratio 1-y2 coordinate in 3D space GO
y2 coordinate of end point of line given direction ratio and y1 coordinate of other end of that line
y2 coordinate in 3D space= Direction ratio 1-y1 coordinate in 3D space GO
z1 coordinate of end point of line given direction ratio and z2 coordinate of other end of that line
z1 coordinate in 3D space= Direction ratio 1-z2 coordinate in 3D space GO
z2 coordinate of end point of line given direction ratio and z1 coordinate of other end of that line
z2 coordinate in 3D space= Direction ratio 1-z1 coordinate in 3D space GO
Projection of line on z axis given length of line & direction ratio of line w.r.to z axis
projection of line=(Direction ratio 3*Length) GO

11 Other formulas that calculate the same Output

Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis
Angle A=acos ((Direction cosine with respect to x axis* Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis* Direction cosine 2 with respect to y axis)+ (Direction cosine with respect to z axis* Direction cosine 2 with respect to z axis)) GO
Angle of intersection between two circles
Angle A=arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between two origin)^2))/(2*Radius 1*Radius 2)) GO
Acute angle of a rhombus if given both diagonals
Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2))) GO
Obtuse angle of rhombus if given both diagonal
Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2))) GO
Acute angle of rhombus given larger diagonal and side
Angle A=(arccos(((Diagonal 1)^2)/(2*(Side of rhombus )^2))-1) GO
One-half obtuse angles in a rhombus if given both diagonals
Angle A=2*(arctan(Diagonal 1/Diagonal 2)) GO
One-half acute angles in a rhombus if given both diagonals
Angle A=2*(arctan(Diagonal 2/Diagonal 1)) GO
Obtuse angle of a rhombus if given area and side
Angle A=asin(Area/Side^2) GO
Acute angle of a rhombus if given area and side
Angle A=asin(Area/Side^2) GO
Angle on the remaining part of the circumference when another angle on same chord is given
Angle A=1*Angle B GO
Angle at another point on circumference when angle on an arc is given
Angle A=1*Angle B GO

Angle between line and plane given coefficients of line and plane Formula

Angle A=asin(((direction ratio 1 of line1*Direction ratio 1)+(direction ratio 2 of line1*Direction ratio 2)+(direction ratio 3 of line1*Direction ratio 3))/(sqrt((direction ratio 1 of line1)^2+(direction ratio 2 of line1)^2+(direction ratio 3 of line1)^2))*(sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2)))
∠A=asin(((a1*d1)+(b1*d2)+(c1*d3))/(sqrt((a1)^2+(b1)^2+(c1)^2))*(sqrt((d1)^2+(d2)^2+(d3)^2)))
More formulas
Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis GO
angle made by direction cosines of two lines in sine form GO
angle between two lines given direction ratios of that two lines w.r.to x, y & z axis GO
Angle between two planes GO

What is plane?

A plane is a surface such that, if two points are taken on it, a straight line joining them lies wholly in the surface. The coefficient of x, y and z in the cartesian equation of a plane are the direction ratios of normal to the plane.

How to Calculate Angle between line and plane given coefficients of line and plane?

Angle between line and plane given coefficients of line and plane calculator uses Angle A=asin(((direction ratio 1 of line1*Direction ratio 1)+(direction ratio 2 of line1*Direction ratio 2)+(direction ratio 3 of line1*Direction ratio 3))/(sqrt((direction ratio 1 of line1)^2+(direction ratio 2 of line1)^2+(direction ratio 3 of line1)^2))*(sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2))) to calculate the Angle A, The Angle between line and plane given coefficients of line and plane formula is defined as the angle made by line x – x1 / a1 = y – y1 / b1 = z – z1 / c1 and plane a2x + b2y + c2z + d2 = 0 form, (eg. direction_ratio_1 is of plane). Angle A and is denoted by ∠A symbol.

How to calculate Angle between line and plane given coefficients of line and plane using this online calculator? To use this online calculator for Angle between line and plane given coefficients of line and plane, enter direction ratio 1 of line1 (a1), Direction ratio 1 (d1), direction ratio 2 of line1 (b1), Direction ratio 2 (d2), direction ratio 3 of line1 (c1) and Direction ratio 3 (d3) and hit the calculate button. Here is how the Angle between line and plane given coefficients of line and plane calculation can be explained with given input values -> 36.15701 = asin(((0.2*0.7)+(0.5*0.2)+(0.7*0.5))/(sqrt((0.2)^2+(0.5)^2+(0.7)^2))*(sqrt((0.7)^2+(0.2)^2+(0.5)^2))).

FAQ

What is Angle between line and plane given coefficients of line and plane?
The Angle between line and plane given coefficients of line and plane formula is defined as the angle made by line x – x1 / a1 = y – y1 / b1 = z – z1 / c1 and plane a2x + b2y + c2z + d2 = 0 form, (eg. direction_ratio_1 is of plane) and is represented as ∠A=asin(((a1*d1)+(b1*d2)+(c1*d3))/(sqrt((a1)^2+(b1)^2+(c1)^2))*(sqrt((d1)^2+(d2)^2+(d3)^2))) or Angle A=asin(((direction ratio 1 of line1*Direction ratio 1)+(direction ratio 2 of line1*Direction ratio 2)+(direction ratio 3 of line1*Direction ratio 3))/(sqrt((direction ratio 1 of line1)^2+(direction ratio 2 of line1)^2+(direction ratio 3 of line1)^2))*(sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2))). direction ratio 1 of line1 is defined as the quotient of two x coordinates of line. , Direction ratio 1 is ratio proportional to direction cosine w.r.to x axis, direction ratio 2 of line1 is defined as the quotient of two y coordinates of line. , Direction ratio 2 is ratio proportional to direction cosine w.r.to y axis, direction ratio 3 of line1 is defined as the quotient of two z coordinates of line. and Direction ratio 3 is ratio proportional to direction cosine w.r.to z axis.
How to calculate Angle between line and plane given coefficients of line and plane?
The Angle between line and plane given coefficients of line and plane formula is defined as the angle made by line x – x1 / a1 = y – y1 / b1 = z – z1 / c1 and plane a2x + b2y + c2z + d2 = 0 form, (eg. direction_ratio_1 is of plane) is calculated using Angle A=asin(((direction ratio 1 of line1*Direction ratio 1)+(direction ratio 2 of line1*Direction ratio 2)+(direction ratio 3 of line1*Direction ratio 3))/(sqrt((direction ratio 1 of line1)^2+(direction ratio 2 of line1)^2+(direction ratio 3 of line1)^2))*(sqrt((Direction ratio 1)^2+(Direction ratio 2)^2+(Direction ratio 3)^2))). To calculate Angle between line and plane given coefficients of line and plane, you need direction ratio 1 of line1 (a1), Direction ratio 1 (d1), direction ratio 2 of line1 (b1), Direction ratio 2 (d2), direction ratio 3 of line1 (c1) and Direction ratio 3 (d3). With our tool, you need to enter the respective value for direction ratio 1 of line1, Direction ratio 1, direction ratio 2 of line1, Direction ratio 2, direction ratio 3 of line1 and Direction ratio 3 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Angle A?
In this formula, Angle A uses direction ratio 1 of line1, Direction ratio 1, direction ratio 2 of line1, Direction ratio 2, direction ratio 3 of line1 and Direction ratio 3. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Angle A=1*Angle B
  • Angle A=1*Angle B
  • Angle A=(arccos(((Diagonal 1)^2)/(2*(Side of rhombus )^2))-1)
  • Angle A=arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between two origin)^2))/(2*Radius 1*Radius 2))
  • Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2)))
  • Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2)))
  • Angle A=asin(Area/Side^2)
  • Angle A=asin(Area/Side^2)
  • Angle A=2*(arctan(Diagonal 2/Diagonal 1))
  • Angle A=2*(arctan(Diagonal 1/Diagonal 2))
  • Angle A=acos ((Direction cosine with respect to x axis* Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis* Direction cosine 2 with respect to y axis)+ (Direction cosine with respect to z axis* Direction cosine 2 with respect to z axis))
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