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Three Dimensional Geometry

Question
CBSEENMA12033270

Find the vector equation for the line passing through the points (– 1, 0, 2) and (3, 4, 6).

Solution
The line passes through the points A(– 1, 0, 2), B(3, 4, 6).
therefore space space space space space space straight a with rightwards arrow on top space equals space minus straight i with hat on top space plus space 2 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 4 space straight j with hat on top space space plus space 6 space straight k with hat on top
where  straight a with rightwards arrow on top comma space straight b with rightwards arrow on top  are position vectors of A and B respectively.
therefore space space space space straight b with rightwards arrow on top minus straight a with rightwards arrow on top space equals space open parentheses 3 space straight i with hat on top space plus space 4 space straight j with hat on top space plus space 6 space straight k with hat on top close parentheses space minus space left parenthesis negative space straight i with hat on top space plus space 2 space straight k with hat on top right parenthesis space equals space 4 space straight i with hat on top space plus space 4 space straight j with hat on top space plus space 4 space straight k with hat on top
Let straight r with rightwards arrow on top be the position vector of any point on the given line. 
∴     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 left parenthesis straight b with rightwards arrow on top minus straight a with rightwards arrow on top right parenthesis
or               straight r with rightwards arrow on top space equals space left parenthesis negative straight i with hat on top space plus space 2 space straight k with hat on top right parenthesis space plus space straight lambda space left parenthesis 4 space straight i with hat on top plus 4 space straight j with hat on top space plus space 4 space straight k with hat on top right parenthesis

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.