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Maths-

General

Easy

Question

If the two adjacent sides of a parallelogram are represented by vectors $stack i with hat on top$ + 2 $stack j with hat on top$ + 3 $stack k with hat on top$ and – 3 $stack i with hat on top$ + 2 $stack j with hat on top$ + $stack k with hat on top$ , then its area is -

5 $\sqrt{6}$
6 $\sqrt{2}$
6 $\sqrt{5}$
200

The correct answer is: 6 $square root of 5$

Let $stack a with rightwards arrow on top$ = $stack i with hat on top$ + 2 $stack j with hat on top$ + 3 $stack k with hat on top$ & $stack b with rightwards arrow on top$ = –3 $stack i with hat on top$ + 2 $stack j with hat on top$ + $stack k with hat on top$
area of parallelogram is | $stack a with rightwards arrow on top$ × $stack b with rightwards arrow on top$ |
 $stack a with rightwards arrow on top$ × $stack b with rightwards arrow on top$ = $open vertical bar table row cell stack i with hat on top end cell cell stack j with hat on top end cell cell stack k with hat on top end cell row 1 2 3 row cell negative 3 end cell 2 1 end table close vertical bar$
= $stack i with hat on top$ (–4) – $stack j with hat on top$ (10) + $stack k with hat on top$ (8)
= – 4 $stack i with hat on top$ – 10 $stack j with hat on top$ + 8 $stack k with hat on top$
 | $stack a with rightwards arrow on top$ × $stack b with rightwards arrow on top$ | = $square root of left parenthesis negative 4 right parenthesis to the power of 2 end exponent plus left parenthesis negative 10 right parenthesis to the power of 2 end exponent plus left parenthesis 8 right parenthesis to the power of 2 end exponent end root$ = 6 $square root of 5$

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