Find the vector equation of line joining the points whose vectors are $2 space straight i with hat on top minus straight j with hat on top plus straight k with hat on top space space and space straight i with hat on top space plus space 2 space straight j with hat on top space minus space 3 space straight k with hat on top.$

Solution

Here, $straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top comma space space space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top space minus space 3 space straight k with hat on top$
The vector equation of line is
$straight r with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space straight lambda space left parenthesis straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top right parenthesis$
or $straight r with rightwards arrow on top space equals space left parenthesis 2 straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top right parenthesis space plus space straight lambda space left parenthesis negative straight i with hat on top space plus space 3 space straight j with hat on top space minus space 4 space straight k with hat on top right parenthesis$

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Three Dimensional Geometry

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