If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to line, x/1 = y/4= z/5 is Q, then PQ is equal to

The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both the lines is

The lines p(p²+ 1) x – y + q = 0 and (p²+ 1)2x + (p²+ 1) y + 2q = 0 are
perpendicular to a common line for

• no value of p

• exactly one value of p

• exactly two values of p

• exactly two values of p

Let the line  lie in the plane x + 3y – αz + β = 0. Then (α, β) equals

• (6, – 17)

• (–6, 7)

• (5, –15)

• (5, –15)

If P and Q are the points of intersection of the circles x²+ y²+ 3x + 7y + 2p – 5 = 0 and x²+ y²+ 2x + 2y – p² = 0, then there is a circle passing through P, Q and (1, 1) for

• all values of p

• all except one value of p

• all except two values of p

• all except two values of p

The shortest distance between the line y – x = 1and the curve x = y² is 

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point . Then

• a = 2, b = 8

• a = 4, b = 6

• a = 6, b = 4

• a = 6, b = 4

If the straight lines  intersect at a point, then the integer k is equal to

• -5

• 2

• 5

• 5

359.

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

• 

• 1/2

• 1

• 1

The resultant of two forces P N and 3 N is a force of 7 N. If the direction of the 3 N force were reversed, the resultant would be N. The value of P is

• 5N

• 6N

• 4N

• 4N