# Find the shortest distance between the lines x + 1 = 2y = – 12z and x = y + 2 = 6z – 6.

OR
From the point P(a, b, c), perpendiculars PL and PM are drawn to YZ and ZX planes
respectively. Find the equation of the plane OLM.

2015
Find the equation of a plane passing through the point P(6, 5, 9) and parallel to
the plane determined by the points A(3, –1, 2), B(5, 2, 4) and C(–1, –1, 6). Also
find the distance of this plane from the point A.
Find the coordinates of the point where the line through the points A(3, 4, 1) and
B(5, 1, 6) crosses the plane determined by the points P(2, 1, 2), Q(3, 1, 0) and
R(4, – 2, 1).

Show that the lines :
r= ^i+j^+^k + (i^–^j+^k)
r= 4^j+ 2^k + μ (2^i–^j+ 3^k ) are coplanar.
Also, find the equation of the plane containing these lines.

A line passing through the point A with position vector

a = 4^i + 2^j + 2^k is parallel to the vector
b= 2^i + 3^j + 6^k . Find the length of the perpendicular drawn on this line from
a point P with position vector
R1 =^i+ 2^j+ 3^k .

Show that four points A, B, C and D whose position vectors are
4^i + 5^j +^k , –^j –^k , 3^i + 9^j + 4^k and 4(–^i +^j +^k ) respectively
are coplanar.

Show that the following two lines are coplanar :

OR
Find the acute angle between the plane 5x – 4y + 7z – 13 = 0 and the y-axis.

Find the direction ratios of the normal to the plane, which passes through
the points (1, 0, 0) and (0, 1, 0) and makes angle with the plane
x + y = 3. Also find the equation of the plane.

– 3. 4) from the point. – 4. 4.Find the distance of the point P(3. – 5) and B(2. . where the line joining the points A(3. 1) intersects the plane 2x + y + z = 7.
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