Question

If vectors $3i+j+5k$ and $ai+bj-15k$ are collinear, then,

• A. $a=3,b=1$
• B. $a=9,b=1$
• C. $a=3,b=3$
• D. $a=9,b=3$

Answer 1

The correct option is D

$a=9,b=3$

Explanation for correct option:

Finding the value of $a$ and $b$:

If the two vectors are collinear then one of them can be expressed as the scalar multiple of the other.

Given vectors$3i+j-5k$ and $ai+bj-15k$ are collinear.

So,

$3i+j-5k=k(ai+bj-15k)$

where $k$ is scalar.

Now comparing both the vectors we get,

$$\begin{gathered} 3=ka...\left(1\right) \\ 1=kb...\left(2\right) \\ -5=-15k \\ \Rightarrow k=\frac{1}{3} \end{gathered}$$

Now substituting the value of $k$ in equation $\left(1\right)$ and $\left(2\right)$ we get,

$a=9b=3$

Hence, the correct option is D.