Class 12

Math

3D Geometry

Three Dimensional Geometry

Write the vector equation of the plane, passing through the point (a,b,c) and parallel to the plane $ri^+j^ +k^˙ =2.$

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Find the direction cosines of the normal to the plane $2x+3y−z=4$.

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

Reduce the equation $2x−3y+5z+4=0$ to intercept form and find the intercepts made by it on the coordinate axes.

Find the equation of the plane passing through the point $(1,−2,7)$ and parallel to the plane $5x+4y−11z=6$.

Prove that the lines $1x =2y−2 =3z+3 $ and $2x−2 =3y−6 =4z−3 $ are coplanar. Also find the equation of the plane containing these lines.

Find the acute angle between the following planes.$r⋅(2i^−3j^ +4k^)=1$ and $r⋅(−i^+j^ )=4$.

A line passes through the point $A(5,−2,4)$ and it is parallel to the vector $(2i^−j^ +3k^ )$. The vector equation of the line is

A line passes through the points $A(2,−1,4)$ and $B(1,2,−2)$. The equations of the line $AB$ are