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Maths-

General

Easy

Question

If $stack a with rightwards arrow on top equals 2 stack i with hat on top plus 5 stack j with hat on top$ and $stack b with rightwards arrow on top equals 2 stack i with hat on top minus stack j with hat on top$ , then the unit vector along $stack a with rightwards arrow on top plus stack b with rightwards arrow on top$ will be

$\frac{\hat{i} - \hat{j}}{\sqrt{2}}$
$\hat{i} + \hat{j}$
$\sqrt{2} (\hat{i} + \hat{j})$
$\frac{\hat{i} + \hat{j}}{\sqrt{2}}$

The correct answer is: $fraction numerator stack i with hat on top plus stack j with hat on top over denominator square root of 2 end fraction$

$stack a with rightwards arrow on top plus stack b with rightwards arrow on top equals 4 stack i with hat on top plus 4 stack j with hat on top$
$fraction numerator stack a with rightwards arrow on top plus stack b with rightwards arrow on top over denominator vertical line stack a with rightwards arrow on top plus stack b with rightwards arrow on top vertical line end fraction equals fraction numerator 4 stack i with hat on top plus 4 stack j with hat on top over denominator square root of 16 plus 16 end root end fraction equals fraction numerator stack i with hat on top plus stack j with hat on top over denominator square root of 2 end fraction$

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The position vectors of P and Q are $5 stack i with hat on top plus 4 stack j with hat on top plus a stack k with hat on top$ and $negative stack i with hat on top plus 2 stack j with hat on top minus 2 stack k with hat on top$ respectively. If the distance between them is 7, then the value of a will be

The position vectors of P and Q are $5 stack i with hat on top plus 4 stack j with hat on top plus a stack k with hat on top$ and $negative stack i with hat on top plus 2 stack j with hat on top minus 2 stack k with hat on top$ respectively. If the distance between them is 7, then the value of a will be

The position vectors of two points A and B are $stack i with hat on top plus stack j with hat on top minus stack k with hat on top$ and $2 stack i with hat on top minus stack j with hat on top plus stack k with hat on top$ respectively. Then $Error converting from MathML to accessible text.$

The position vectors of two points A and B are $stack i with hat on top plus stack j with hat on top minus stack k with hat on top$ and $2 stack i with hat on top minus stack j with hat on top plus stack k with hat on top$ respectively. Then $Error converting from MathML to accessible text.$

Let | $stack a with rightwards arrow on top$ | = 1, | $stack b with rightwards arrow on top$ | = 2, | $stack c with rightwards arrow on top$ | = 3 and $stack a with rightwards arrow on top$  ( $stack b with rightwards arrow on top$ + $stack c with rightwards arrow on top$ ), $stack b with rightwards arrow on top$  ( $stack c with rightwards arrow on top$ + $stack a with rightwards arrow on top$ ), $stack c with rightwards arrow on top$  ( $stack a with rightwards arrow on top$ + $stack b with rightwards arrow on top$ ) then | $stack a with rightwards arrow on top$ + $stack b with rightwards arrow on top$ + $stack c with rightwards arrow on top$ | =

Let | $stack a with rightwards arrow on top$ | = 1, | $stack b with rightwards arrow on top$ | = 2, | $stack c with rightwards arrow on top$ | = 3 and $stack a with rightwards arrow on top$  ( $stack b with rightwards arrow on top$ + $stack c with rightwards arrow on top$ ), $stack b with rightwards arrow on top$  ( $stack c with rightwards arrow on top$ + $stack a with rightwards arrow on top$ ), $stack c with rightwards arrow on top$  ( $stack a with rightwards arrow on top$ + $stack b with rightwards arrow on top$ ) then | $stack a with rightwards arrow on top$ + $stack b with rightwards arrow on top$ + $stack c with rightwards arrow on top$ | =

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