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Vector Algebra

Question
CBSEENMA12034219
Wired Faculty App

Find the area of the triangle formed by O, A, B. when OA with rightwards arrow on top space equals space straight i with hat on top plus 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space space space OB with rightwards arrow on top space equals space minus 3 space straight i with hat on top space minus space 2 straight j with hat on top space plus space straight k with hat on top

Solution
OA with rightwards arrow on top space equals space straight i with hat on top plus 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space space space OB with rightwards arrow on top space equals space minus 3 space straight i with hat on top space minus space 2 straight j with hat on top space plus space straight k with hat on top OA with rightwards arrow on top space cross times space OB with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell space straight j with hat on top end cell cell space straight k with hat on top end cell row cell space 1 end cell cell space 2 end cell cell space 3 end cell row cell negative 3 end cell cell space minus 2 end cell cell space 1 end cell end table close vertical bar space equals space straight i with hat on top space open vertical bar table row 2 3 row cell negative 2 end cell 1 end table close vertical bar minus straight j with hat on top space open vertical bar table row cell space 1 end cell cell space 3 end cell row cell negative 3 end cell cell space 1 end cell end table close vertical bar space plus straight k with hat on top space open vertical bar table row 1 cell space space space space space 2 end cell row cell negative 3 end cell cell space space minus 2 end cell end table close vertical bar space space space space space space space space space space space space space space space space equals left parenthesis 2 plus 6 right parenthesis space straight i with hat on top space minus left parenthesis 1 plus 9 right parenthesis space straight j with hat on top space plus space left parenthesis negative 2 plus 6 right parenthesis space straight k with hat on top space equals 8 space straight i with hat on top space minus space 10 space straight j with hat on top space plus space 4 space straight k with hat on top therefore space space space space open vertical bar OA with rightwards arrow on top space cross times space OB with rightwards arrow on top close vertical bar space equals space square root of 64 plus 100 plus 16 end root space equals space square root of 180 space equals space square root of 36 space cross times 5 end root space equals space 6 square root of 5 Area space of space increment OAB space equals space 1 half open vertical bar OA with rightwards arrow on top space cross times space OB with rightwards arrow on top close vertical bar space equals space 1 half 6 square root of 5 space equals space 3 square root of 5 space sq. space units.

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