Question

If $a$ vector of magnitude $50$ is collinear with the vector$b=6i-8j-15/2k$ and makes an acute angle with the positive direction of the Z-axis, then the vector $a$ is equal to?

• A. $a=4b$
• B. $a=-4b$
• C. $b=4a$
• D. None of these

Answer 1

The correct option is B

$a=-4b$

Explanation for correct option:

Find the vector $a$:

Given that $a$vector of magnitude$50$ is collinear with the vector$b=6i-8j-15/2k$.

$$\begin{gathered} \Rightarrow a=kb \\ \Rightarrow a=k\left|b\right| \\ \Rightarrow 50=k\sqrt{6^2+8^2+{\left(\frac{15}{2}\right)}^2} \\ \Rightarrow 50=k\frac{\sqrt{625}}{2} \\ \Rightarrow k=100/25=4 \end{gathered}$$

Vector makes an acute angle with the positive direction of the Z-axis

$a.k=$positive

$$\begin{gathered} \Rightarrow k<0 \\ \Rightarrow k=-4 \\ \Rightarrow a=-4b \end{gathered}$$

Hence,the correct option is B.