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Vector Algebra

Question
CBSEENMA12034209
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Find the area of the parallelogram determined by the vectors 3 space straight i with hat on top space plus space 4 space straight j with hat on top space and space straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top.

Solution

Let straight a with rightwards arrow on top space equals space 3 straight i with hat on top plus 4 straight j with hat on top comma space space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus straight j with hat on top space plus space straight k with hat on top
             straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 3 4 0 row 1 1 1 end table close vertical bar space equals space straight i with hat on top space open vertical bar table row 4 0 row 1 1 end table close vertical bar space minus space straight j with hat on top space open vertical bar table row 3 0 row 1 1 end table close vertical bar plus straight k with hat on top space open vertical bar table row 3 4 row 1 1 end table close vertical bar space space space space space space space space space space space space space space equals left parenthesis 4 minus 0 right parenthesis space straight i with hat on top space minus space left parenthesis 3 minus 0 right parenthesis space straight j with hat on top space plus space left parenthesis 3 minus 4 right parenthesis space straight k with hat on top space equals space 4 space straight i with hat on top space minus space 3 space straight j with hat on top space minus space straight k with hat on top therefore space space space space space space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of 16 plus 9 plus 1 end root space equals space square root of 26 therefore space space area space of space parallelogram space equals space square root of 26 space sq. space units. space

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