class 12

Math

3D Geometry

Three Dimensional Geometry

The length of the projection of the line segment joining the points $(5,−1,4)$ and $(4,−1,3)$ on the plane $x+y+z=7$ is

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Find the Cartesian and vector equations of a plane passing through the point $(1,2,−4)$ and parallel to the lines $2x−1 =3y−2 =6z+1 $ and $1x−1 =1y+3 =−1z $.

Find the vector equation of a plane whose Cartesian equation is $5x−7y+2z+4=0$.

Find the equation of a plane passing through the points $A(a,0,0),B(0,b,0)$ and $C(0,0,c)$.

Show that the following pairs of planes are at right angles.$x−2y+4z=10$ and $18x+17y+4z=49$.

Find the equation of the plane passing through the point $(1,4,−2)$ and parallel to the plane $2x−y+3z+7=0$.

Find the acute angle between the following planes.$2x−y+z=5$ and $x+y+2z=7$.

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 of the plane $4x−3y+2z$ to the intercept form, and hence find the intercepts made by the plane with the coordinate axes.