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Direction Angle, Direction cosine - Vector Algebra Video Lecture - Class 12

FAQs on Direction Angle, Direction cosine - Vector Algebra Video Lecture - Class 12

1. What is the direction angle of a vector?
Ans. The direction angle of a vector is the angle measured between the positive x-axis and the line segment representing the vector in the xy-plane.
2. How is the direction angle calculated for a vector?
Ans. The direction angle of a vector can be calculated using the formula: direction angle = arctan(y/x), where x and y are the components of the vector in the xy-plane.
3. What are direction cosines of a vector?
Ans. Direction cosines of a vector are the cosines of the angles made by the vector with the positive x, y, and z-axes (or any other set of mutually perpendicular axes). They are denoted by l, m, and n respectively.
4. How to find the direction cosines of a vector?
Ans. To find the direction cosines of a vector, divide each component of the vector by its magnitude. The resulting ratios will give the direction cosines of the vector. For example, if the vector is (a, b, c), then the direction cosines are: l = a/|v|, m = b/|v|, n = c/|v|, where |v| is the magnitude of the vector.
5. How are direction cosines related to the direction angle?
Ans. The direction cosines l, m, and n can be related to the direction angle θ using the following equations: l = cos(θ), m = sin(θ)cos(φ), n = sin(θ)sin(φ), where φ is the angle made by the projection of the vector on the xy-plane with the positive x-axis.
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