Question

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

• 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 $a=9,b=3$

Since the vectors $3i+j-5k$ and $ai+bj-15k$ are co-linear, then one of them can be expressed as the scalar multiple of the other.

Then,

$3i+j-5k$$=\lambda (ai+bj-15k)$ [ $\lambda$ being a scalar]

Comparing both sides the co-efficient of $i,j,k$ we get,

$3=\lambda a$.....(1) $1=\lambda b$......(2) $-5=-15\lambda \Rightarrow \lambda =\frac{1}{3}$

Using this value of $\lambda$ from (1) and (2) we get,

$a=9,b=3$