Question

Compute the orthogonal projection of a vector onto the line through a point and the origin

A) Dot product of the vector and the line
B) Cross product of the vector and the line
C) Scalar projection of the vector onto the line
D) Matrix multiplication of the vector and the line

Answer 1

The orthogonal projection of a vector onto a line can be computed using the scalar projection of the vector onto the line. Hence the correct answer is option C

Step-by-step explanation:

The orthogonal projection of a vector onto the line through a point and the origin can be computed using the scalar projection of the vector onto the line. The scalar projection is obtained by taking the dot product of the vector and the line. The dot product is computed by multiplying the magnitudes of the vector and the line by the cosine of the angle between them.

For example, if vector V is projected onto the line with direction vector D, the scalar projection P is given by:

P = V ● D / |D|

Hence the correct answer is option C