1.
Find the length of the perpendicular drawn from the origin to the plane 2x-3y + 6z + 21 = 0.
2.
Write the direction cosines of the vector -2i + j – 5k
3.
Find the coordinates of the point, where the line intersects the plane x – y + z – 5 = 0. Also find the angle between the line & the plane.
4.
If a line makes angles 90^{0}, 135^{0}, 45^{0} with x, y, and z-axes respectively, find its direction cosines.
5.
Find the vector equation of the plane which contains the line of intersection of the planes
& which is perpendicular to the plane
6.
There are two lines in which one line is passing through the points (4, 7, 8) (2, 3, 4) & another line is passing through the points (-1, -2, 1), (1, 2, 5). What is true regarding these lines?
A.
B.
AB is perpendicular to CD
C.
AB is inclined to CD at certain angle
D.
7.
Find the angle between the following pair of lines:
8.
Find the Cartesian equation of the line which passes through the point (-2, 4, -5) and is parallel to the line:
9.
Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0
10.
Find the coordinates of the point where the line through (3, -4, -5) and (2, -3, 1) crosses the plane, passing through the points (2, 2, 1), (3, 0, 1) and (4, -1, 0).
11.
Find the Cartesian equation of the plane which contains the line of intersection of the planes
12.
Show that the lines
are intersecting. Hence find their point of intersection.
13.
Find the vector equation of the plane through the points (2, 1,-1) and (-1, 3, 4) and perpendicular to the plane x -2y+ 4z = 10.
14.
Find the shortest distance between the lines:
15.
Find the equation of the plane passing through the line of intersection of the planes
whose perpendicular distance from origin is unity.