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Vector Algebra

Question
CBSEENMA12033983

Find the vector joining the points P(2, 3, 0) and Q (– 1, – 2,  – 4) directed from P to Q.

Solution
P(2, 3, 0), Q(– 1, – 2. – 4) are two given points
therefore space space space space space space PQ with rightwards arrow on top space equals space left parenthesis negative 1 minus 2 right parenthesis space straight j with hat on top space plus space left parenthesis negative 2 minus 3 right parenthesis space straight j with hat on top space plus space left parenthesis negative 4 minus 0 right parenthesis space straight k with hat on top                                                                                       open square brackets because space space space PQ with rightwards arrow on top space equals space left parenthesis straight x subscript 2 minus straight x subscript 1 right parenthesis space straight i with hat on top space plus space left parenthesis straight y subscript 2 minus straight y subscript 1 right parenthesis space straight j with hat on top space plus space left parenthesis straight z subscript 2 minus straight z subscript 1 right parenthesis space straight k with hat on top close square brackets  
i.e.,   PQ with rightwards arrow on top space equals space minus 3 straight i with hat on top space minus space 5 straight j with hat on top space minus space 4 straight k with hat on top.