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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Bihar CECEBihar CECE 2011

Solution:

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