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Maths-

General

Easy

Question

Let $stack a with rightwards arrow on top equals stack i with hat on top plus stack j with hat on top plus 2 stack k with hat on top text end text$ and $stack b with rightwards arrow on top equals 2 stack i with hat on top minus stack j with hat on top minus stack k with hat on top$ . Then the point of intersection of the
lines $stack r with rightwards arrow on top cross times stack a with rightwards arrow on top equals stack b with rightwards arrow on top cross times stack a with rightwards arrow on top$ and $stack r with rightwards arrow on top cross times stack b with rightwards arrow on top equals stack a with rightwards arrow on top cross times stack b with rightwards arrow on top$ is

$- \hat{i} + 2 \hat{j} + 3 \hat{k}$
$\hat{i} - 2 \hat{j} - 3 \hat{k}$
$\hat{i} + \hat{k}$
$- 3 \hat{i} - \hat{k}$

The correct answer is: $stack i with hat on top plus stack k with hat on top$

$stack r with rightwards arrow on top cross times stack a with rightwards arrow on top equals stack b with rightwards arrow on top cross times stack a with rightwards arrow on top left parenthesis stack r with rightwards arrow on top minus stack b with rightwards arrow on top right parenthesis stack a with rightwards arrow on top$ = $stack 0 with rightwards arrow on top$
$stack r with rightwards arrow on top minus stack b with rightwards arrow on top equals lambda stack a with rightwards arrow on top stack r with rightwards arrow on top equals stack b with rightwards arrow on top plus lambda stack a with rightwards arrow on top$  R
Similarly equation of second line is
 $stack r with rightwards arrow on top equals stack a with rightwards arrow on top plus mu stack b with rightwards arrow on top$  R
For point of intersection
$stack b with rightwards arrow on top plus lambda stack a with rightwards arrow on top equals stack a with bar on top plus mu stack b with rightwards arrow on top$ for suitable values of  &.
(1- ) $stack b with rightwards arrow on top plus left parenthesis lambda minus 1 right parenthesis stack a with rightwards arrow on top$ = 0
1 -  =  - 1 = 0
(as $stack a with rightwards arrow on top text and end text stack b with rightwards arrow on top$ are non-collinear)
 = = 1.
Point of intersection = $stack a with rightwards arrow on top plus stack b with rightwards arrow on top equals 3 stack i with hat on top plus stack k with hat on top$

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