class 12

Math

3D Geometry

Three Dimensional Geometry

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzplane at the point $(0,217 ,2−13 )$.Then

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Let L be the line of intersection of the planes 2x+3y+z=1 andx+3y+2z=2. If L makes an angle α with the positive x-axis, then cos αequals

The vector a⃗ =αi^+2j^+βk^ lies in the plane of the vectors b⃗ =i^+j^ and c⃗ =j^+k^ and bisects the angle between b⃗ andc⃗ . Then which one of the following gives possible values of a and b?

Find the values $p$ so that line $31−x =2p7y−14 =2z−3 and3p7−7x =1y−5 =56−z $ are at right angles.

Find the equation of the plane containing the lines $4x−5 =4y−7 =−5z+3 and7x−8 =1y−4 =3z−5 ˙$

The line, x−23=y+12=z−1−1 intersects the curve xy=c2,z=0 if c is equal to

If Q is the image of the point P(2, 3, 4) under the reflection in the plane x−2y+5z=6, then the equation of the line PQis

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

The plane which passes through the point $(3,2,0)$ and the line $1x−3 =5y−6 =4z−4 $ is a. $x−y+z=1$ b. $x+y+z=5$ c. $x+2y−z=1$ d. $2x−y+z=5$