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Vector Algebra

Question
CBSEENMA12034218
Wired Faculty App

Find the area of the triangle whose adjacent sides are made by the vectors 

Solution
straight a with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space straight j with hat on top space plus space 4 space straight k with hat on top comma space space space space straight b with rightwards arrow on top space equals space straight i with hat on top space minus space 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 1 4 row 1 cell negative 1 end cell 1 end table close vertical bar space equals space straight i with hat on top space open vertical bar table row 1 4 row cell negative 1 end cell 1 end table close vertical bar space minus straight j with hat on top space open vertical bar table row 3 4 row 1 1 end table close vertical bar space plus space straight k with hat on top space open vertical bar table row 3 1 row 1 cell negative 1 end cell end table close vertical bar space space space space space space space space space space space space space equals space left parenthesis 1 plus 4 right parenthesis space straight j with hat on top space minus space left parenthesis 3 minus 4 right parenthesis space straight j with hat on top space plus left parenthesis negative 3 minus 1 right parenthesis space straight k with hat on top space equals space 5 space straight i with hat on top space plus space straight j with hat on top space minus 4 space straight k with hat on top space therefore 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 25 plus 1 plus 16 end root space equals space square root of 42
Required area of triangle  = 1 half open vertical bar straight a with rightwards arrow on top cross times straight b with rightwards arrow on top close vertical bar space equals space 1 half square root of 42 space sq. space units.

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