Question

Let $\vec{a}=i+2 j+2 k$ and $\vec{b}=3 i+6 j+2 k$. Then the vector in the direction of $\vec{a}$ having magnitude equal to the magnitude of $\vec{b}$ is

• A. $7(i+2 j+2 k)$
• B. $\frac{7}{3}(i+2 j+2 k)$
• C. $\frac{7}{3}(i+2 j+3 k)$
• D. $\frac{7}{9}(i+2 j+2 k)$

Answer 1

Answer: (B)

Vector in the direction of $\vec{a}$ having magnitude equal to the magnitude of
$\vec{b}= \frac{\vec{a}}{|\vec{a}|}|\vec{b}|$
$=\frac{(i+2 j+2 k)}{\sqrt{9}} \sqrt{9+36+4}=\frac{7}{3}(i+2 j+2 k)$