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Vector Algebra

Question
CBSEENMA12035730

If a unit vector straight a with rightwards arrow on top space equals space straight x straight i with hat on top plus 2 straight j with hat on top minus straight z straight k with hat on top and straight b with rightwards arrow on top space equals space 3 straight i with hat on top minus straight y straight j with hat on top plus straight k with hat on top are two equal vectors, then write the value of x+y+z.

Solution

Given that straight a with rightwards arrow on top equals straight x straight i with hat on top plus 2 straight j with hat on top minus straight z straight k with hat on top and straight b with rightwards arrow on top equals 3 straight i with hat on top minus straight y straight j with hat on top plus straight k with hat on top are equal vectors.
therefore space straight x straight i with hat on top plus 2 straight j with hat on top minus straight z straight k with hat on top space equals space 3 straight i with hat on top minus straight y straight j with hat on top plus straight k with hat on top
rightwards double arrow straight x equals space 3 comma space space straight y space equals space minus 2 comma space space straight z equals space minus 1
therefore space space straight x plus straight y plus straight z space equals space 3 plus left parenthesis negative 2 right parenthesis plus left parenthesis negative 1 right parenthesis space equals space 0