Question

If $a=2i+2j+3k,b=-1+2j+k$ and $c=3i+j$, then $a+tb$ this perpendicular to $c$; if $t$ is equal to

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is D 8

Given, $a=2i+2j+3k,b=-1+2j+k$ and $c=3i+j$

We need to find value of $a+tb\perp c$
$\Rightarrow (a+tb)\cdot c=0$
$\Rightarrow a\cdot c+tb\cdot c=0$
$\Rightarrow t=-\frac{a\cdot c}{b\cdot c}$
$\Rightarrow t=-\frac{(2i+2j+3k)\cdot (3i+j)}{(-i+2j+k)\cdot (3i+j)}$
$\Rightarrow t=-\frac{6+2+0}{-3+2+0}=8$