Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the vector equation of a line passing through the point $(1,2,3)$ and parallel to the vector $(3i^+2j^ −2k^ )$

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Find the radius of the circular section of the sphere $∣r∣=5$ by the plane $ri^+2j^ −k^˙ =43 ˙$

Under which one of the following condition will the two planes x+y+z=7 andαx+βy+γz=3, be parallel (but not coincident)?

Which one of the following is the plane containing the lien x−22=y−33=z−45 and parallel to z axis?

The lines which intersect the skew lines $y=mx,z=c;y=−mx,z=−c$ and the x-axis lie on the surface: (a.) $cz=mxy$ (b.) $xy=cmz$ (c.) $cy=mxz$ (d.) none of these

Find the equation of a line which passes through the point $(2,3,4)$ and which has equal intercepts on the axes.

The Cartesian equation of a line is $2x−3 =−2y+1 =5z−3 $ . Find the vector equation of the line.

Find the equation of the sphere which has centre at the origin and touches the line $2(x+1)=2−y=z+3.$

Consider the following relations among the anglesα, β and γ made by a vector with the coordinate axes$I.cos2α+cos2β+cos2γ=−1$II. sin2α+sin2β+sin2γ=1$Whichoftheaboveias recorrect?$