Question

A vector which makes equal angle with the vectors $1/3(i-2j+2k),1/5(-4i-3k)$ and $j$ is

• A. 5i+j+jk
• B. -6i+j+5k
• C. 5i-j-5k
• D. 5i+j-5k

Answer 1

Answer: (C)

Let the required vector be $a=xi+yj+zk$.
It makes equal angles with the vectors
$b=\frac{1}{3}(i-2j+2k)$
$c=\frac{1}{5}(-4i-3k),d=j$
$\therefore a.b=a.c=a.d[\because b,c,d$ are unit vectors $]$
If $a.b=a.d$, then
$\frac{1}{3}(x-2y+2z)=y$
If $a.c=a.d$, then
$\frac{1}{5}(-4x-3z)=y$
$\Rightarrow x-5y+2z=0$
and $4x+5y+3z=0$
Solving these equation, we get
$x=-z$ and $x=-5y$
$\therefore \frac{x}{-5}=\frac{y}{1}=\frac{z}{5}$
$\Rightarrow \frac{x}{5}=\frac{y}{-1}=\frac{z}{-5}$
$\therefore a=-5i+j+5k$
or $a=5i-j-5k$