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Maths-

General

Easy

Question

Given two vectors $stack i with hat on top minus stack j with hat on top$ and $stack i with hat on top minus 2 stack j with hat on top$ , then unit vector coplanar with two vectors and perpendicular to first is

$= \frac{1}{3} | \vec{b} | | \vec{c} | \vec{a}$
$\frac{1}{\sqrt{5}} (2 \hat{i} + \hat{j})$
$\pm \frac{1}{\sqrt{2}} (\hat{i} + \hat{k})$
None of these

The correct answer is: $equals fraction numerator 1 over denominator 3 end fraction vertical line stack b with rightwards arrow on top vertical line vertical line stack c with rightwards arrow on top vertical line stack a with rightwards arrow on top$

$stack a with rightwards arrow on top cross times left parenthesis stack a with rightwards arrow on top cross times stack b with rightwards arrow on top right parenthesis$ = $left parenthesis stack a with rightwards arrow on top. stack b with rightwards arrow on top right parenthesis stack a with rightwards arrow on top – left parenthesis stack a with rightwards arrow on top. stack a with rightwards arrow on top right parenthesis stack b with rightwards arrow on top$
$equals 3 left parenthesis stack i with hat on top – stack j with hat on top right parenthesis – 2 left parenthesis stack i with hat on top – 2 stack j with hat on top right parenthesis equals stack i with hat on top plus stack j with hat on top$
unit vector = ± $fraction numerator stack a with rightwards arrow on top cross times left parenthesis stack a with rightwards arrow on top cross times stack b with rightwards arrow on top right parenthesis over denominator vertical line stack a with rightwards arrow on top cross times left parenthesis stack a with rightwards arrow on top cross times stack b with rightwards arrow on top right parenthesis vertical line end fraction$ $equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction left parenthesis stack i with hat on top plus stack j with hat on top right parenthesis$

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If vectors $Error converting from MathML to accessible text.$ and $Error converting from MathML to accessible text.$ are the sides of ABC, then the length of the median through A is:

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