Question

A vector a which is collinear with the vector $6i-8j-\frac{15}{2}k$ of magnitude $50$ making on obtuse angle with z-axis is

• A. $24i-32j-30k$
• B. $-24i+32j+30k$
• C. $24i+32j-30k$
• D. none of these

Answer 1

Answer: (A)

$24i-32j-30k$

A vector which is collinear with the vector $6i-8j-\frac{15}{2}k$ is $\lambda \left(6i-8j-\frac{15}{2}k\right)$

magnitude of $\lambda \left(6i-8j-\frac{15}{2}k\right)$ is 50

$\Rightarrow \lambda \sqrt{36+64+\frac{225}{4}}=50$

$\Rightarrow \lambda =4$

$\therefore$ required vector is $24i-32j-30k$ ( as z component is less than $0$, it makes obtuse angle with z-axis)