Question

If $(1,2,4)$ and $(2,-3\lambda ,-3)$ are the initial and terminal points of the vector $i+5j-7k$, then the value of $\lambda$ is

• A. $\frac{7}{3}$
• B. $\frac{-7}{3}$
• C. $\frac{-5}{3}$
• D. $\frac{5}{3}$
• E. $\frac{-7}{5}$

Answer 1

Answer: (B)

$\frac{-7}{3}$

Let $OA=i+2j+4k$
and $OB=2i-3\lambda j-3k$
Given, $AB=i+5j-7k$
$\Rightarrow OB-OA=i+5j+7k$
$\Rightarrow i+(-3\lambda -2)j-7k=i+5j-7k$
On comparing the coefficient of $j$, we get
$-3\lambda -2=5$
$\Rightarrow \lambda =\frac{-7}{3}$