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Three Dimensional Geometry

Question
CBSEENMA12033433

Find the vector equations of the plane passing through the points R(2, 5, –3), S(– 2, – 3, 5) and T(5, 3, – 3).

Solution

Here,   straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 3 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space minus 2 space straight i with hat on top space minus space 3 space straight j with hat on top space minus space 5 space straight k with hat on top comma space space straight c with rightwards arrow on top space equals space 5 space straight i with hat on top space plus space 3 space straight j with hat on top space minus space 3 space straight k with hat on top
where straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top are position vectors  of R, S, T respectively.
The vector equation of plane is
               open parentheses straight r with rightwards arrow on top space minus space straight a with rightwards arrow on top close parentheses space. space open parentheses straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top close parentheses space cross times space left parenthesis straight c with rightwards arrow on top space minus space stack straight a right parenthesis with rightwards arrow on top space equals space 0
or         open square brackets straight r with rightwards arrow on top space minus space left parenthesis 2 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 3 space straight k with hat on top right parenthesis close square brackets. space space space open square brackets left parenthesis negative 4 space straight i with hat on top space minus space 8 space straight j with hat on top space minus space 2 space straight k with hat on top space right parenthesis cross times space left parenthesis 3 space straight i with hat on top space minus space space 2 space straight j with hat on top right parenthesis close square brackets space equals space 0

Some More Questions From Three Dimensional Geometry Chapter

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