Question

Given the vectors $\overrightarrow{a}=(3,-1,5)$ and $\overrightarrow{b}=(1,2,-3)$ . A vector $\overrightarrow{c}$ is such that it is perpendicular to the $z-axis$ and satisfies the conditions $\overrightarrow{c}.\overrightarrow{a}=9$ and $\overrightarrow{c}.\overrightarrow{b}=-4$ . Then $\overrightarrow{c}$ is equal to

• A. (2, 3, 0)
• B. (2, -3, 1)
• C. (2,-3. 0)
• D. none of these.

Answer 1

Answer: (C)

$\vec{c}$ can be $\left(-2,3,0\right)$ or $\left(2,-3,0\right)$ since it is $\perp$ to $\left(0,0,1\right)$ i.e., $z$-axis
Since $\vec{c}.\vec{a}=9$ and $\vec{c}.\vec{b}=-4$
$\therefore \vec{c}=\left(2,-3,0\right)$
$[\because (2,-3,0)\cdot (3,-1,5)=6+3=9$$(2,-3,0)\cdot (1,2,-3)=2-6=-4]$