Question

Given two vectors A and B, show that the vector component of A perpendicular to B is C=A−A.B/B.​B B

Answer 1

To find the vector component of vector A perpendicular to vector B, subtract the component of A along the direction of B from A itself.

Step-by-step explanation:

The vector component of vector A perpendicular to vector B can be found by subtracting the component of A along the direction of B from vector A itself. This can be expressed as:

C = A - (A · B/B) · B

Here, A · B represents the dot product of vectors A and B, which gives the magnitude of the projection of A onto B. Dividing this by the magnitude of B gives the unit vector in the direction of B. Multiplying this unit vector by A · B/B then gives the component of A along the direction of B. Subtracting this component from A gives the vector component of A perpendicular to B, which is C.