Question

what is the best approximation of the projection of (2,6) onto (5,-1)?
A. 0.10(2,6)
B. 0.15(5,-1)
C. 0.10(5,-1)
D. 0.15(2,6)

Answer 1

Projection of vector A onto B is given by the formula:
\[
\frac{A \cdot B}{|B|} * \frac{B}{|B|} \\
\text{ } \\
\text{Note: }\frac{A \cdot B}{|B|}
\text{ is the scalar projection of A onto B or the component of A }\\
\text{in the direction of B and }
\frac{B}{|B|} ~\text{is the unit vector in the direction of B. } \\
\text{Here, }A = <2, 6>; ~~B = <5, -1> \\
\text{Plug A and B into the formula, do the dot product and the rest and simplify.}
\]