class 12

Math

3D Geometry

Three Dimensional Geometry

The distance of the point $(1,−5,9)$from the plane $x−y+z=5$measured along the line $x=y=z$is :

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Find the equation of the plane passing through the points $A(−1,1,1)$ and $B(1,−1,1)$ and perpendicular to the plane $x+2y+2z=5$.

If O be the origin and $P(1,2,−3)$ be a given point, then find the equation of the plane passing through P and perpendicular to OP.

The equations of a line are $24−x =2y+3 =1z+2 $. Find the direction cosines of a line parallel to this line.

Find the vector equation of a line passing through the point $(2i^−3j^ −5k^)$ and perpendicular to the plane $r⋅(6i^−3j^ +5k^)+2=0$.Also, find the point of intersection of this line and the plane.

If a line makes angles $α,β$ and $γ$ with the x-axis, y-axis and z-axis respectively then $(sin_{2}α+sin_{2}β+sin_{2}γ )=$

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Find the equation of the plane passing through the point $A(−1,−1,2)$ and perpendicular to each of the planes $3x+2y−3z=1$ and $5x−4y+z=5$.

Find the equation of the plane through the points $A(2,1,−1)$ and $B(−1,3,4)$ and perpendicular to the plane $x−2y+4z=10$. Also, show that the plane thus obtained contains the line.$r=(−i^+3j^ +4k^)+λ(3i^−2j^ −5k^)$.