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Vector Algebra

Question
CBSEENMA12033945
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The position vectors of points A. B, C. D) are straight a with rightwards arrow on top comma space space straight b with rightwards arrow on top comma space space 2 space straight a with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top  and  straight a with rightwards arrow on top space minus space 2 space straight b with rightwards arrow on top respectively, show that AC with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top space and space DB with rightwards arrow on top space equals space 3 space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top

Solution

Here P.V. of straight A space equals space straight a with rightwards arrow on top.     P.V. of B = straight b with rightwards arrow on top,     P.V. of C = 2 space straight a with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top.
                   P.V. of  D = straight a with rightwards arrow on top space minus space 2 space straight b with rightwards arrow on top
          therefore space space space space space AC with rightwards arrow on top space equals space straight P. straight V. space of space straight C space minus space straight P. straight V. space of space straight A space equals space open parentheses 2 space stack straight a space with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top close parentheses space minus space straight a with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space 3 space straight b with rightwards arrow on top space space space space space space space space space space space space DB with rightwards arrow on top space equals space straight P. straight V. space of space straight B space minus space straight P. straight V. space of space straight D space equals space straight b with rightwards arrow on top space minus space left parenthesis straight a with rightwards arrow on top space minus space 2 space straight b with rightwards arrow on top right parenthesis space equals space 3 space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top

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