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In the following cases, find the distan...

In the following cases, find the distance of each of the given points from the corresponding given plane. Point Plane
(a) `(0, 0, 0)` , `3x+4y + 12 z = 3`
(b) `(3, 2, 1)` , `2x +y + 2z + 3 = 0`
(c) `(2, 3,-5)` , `x+ 2y +-2z = 9`
(d) `(6 , 0 , 0) ` , `2x - 3y + 6z -2 = 0`

Text Solution

Verified by Experts

we know,
`d=|(a_2x_1+b_2y_1+c_2z_1+d)/sqrt(a^2+b^2+c^2)|`
1)`d=|(-3)/sqrt(3^2+4^2+12^2)|=13/3`
2)`d=|(-13)/sqrt(9)|=13/3`
3)`d=|9/sqrt9|=9/3=3`
4)`d=|-14/7|=2`
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