Class 12

Math

3D Geometry

Three Dimensional Geometry

A line $OP$ through origin $O$ is inclined at $30_{0}and45_{0}→OXandOY,$ respectivley. Then find the angle at which it is inclined to $OZ˙$

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A line makes angles, θ,ϕ and ψ with x, y, z axes respectively. Consider the following:$1.sin2θ+sin2ϕ=cos2ψ$2. cos2θ+cos2ϕ=sin2ψ$3.sin2θ+cos2ϕ=cos2ψ$Which of the above is/are correct?

Find the angel between the planes $2x+y−2x+3=0andr6i^+3j^ +2k^˙ =5.$

Find the radius of the circular section in which the sphere $∣r∣=5$ is cut by the plane $ri^+j^ +k^˙ =33. $

The line joining the points $(−2,1,−8)and(a,b,c)$ is parallel to the line whose direction ratios are $6,2,and3.$ Find the values of $a,bandc$

A mirror and source of light are situated at the origin O and a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are $1,−1,1,$ then DCs for the reflacted ray are :

Show that $ax+by+r=0,by+cz+p=0andcz+ax+q=0$ are perpendicular to $x−y,y−zandz−x$ planes, respectively.

A line passes through the points $(6,−7,−1)and(2,−3,1)˙$ Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.

Find the coordinates of a point on the $2x−1 =−3y+1 =z$ atg a distance $414 $ from the point $(1,−1,0)˙$