Archives

The image of the point (1, 3, 4) with respect to the plane 2x – y + z + 3 = 0 is

1) (-1, 4, 3) 2) (-3, 5, 2) 3) (1, 3, 4) 4) (-1, -3, -4) Solution: (2) (-3, 5, 2) The equation of a line through the point P (1, 3, 4) and... View Article

The plane ax + by + cz = 1 meets the coordinates axes at A, B and C. The centroid of ∆ABC is

1) (3a, 3b, 3c) 2) (a / 3, b / 3, c / 3) 3) (1 / 3a, 1 / 3b, 1 / 3c) 4) (a, b, c) Solution: (3) (1 / 3a, 1 / 3b, 1 / 3c) The... View Article

A equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

1) x - 2y + 2z ± 3 = 0 2) x - 2y + 2z + 1 = 0 3) x - 2y + 2z - 1 = 0 4) x - 2y + 2z + 5 = 0 Solution: (1) x - 2y + 2z ± 3 = 0... View Article

The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2, x – y + z = 3 and at a distance 2/√3 from the point (3, 1, -1), is

1) 5x - 11y + 17z = 0 2) √2x + y = 3√2 - 1 3) x + y + z = √3 4) x - √2y = 1 - √2 Solution: (1) 5x - 11y + 17z = 0... View Article

Foot of the perpendicular drawn from the origin to the plane 2x – 3y + 4z = 29 is

1) (5, -1, 4) 2) (7, -1, 3) 3) (5, -2, 3) 4) (2, -3, 4) 5) (1, -3, 4) Solution: (4) (2, -3, 4)... View Article

The image of the point with position vector i + 3k in the plane r. (i + j + k) = 1 is

1) i + 2j + k 2) i + 2j - k 3) - i - 2j + k 4) i - 2j + k Solution: (3) - i - 2j + k... View Article

The equation of the plane through the intersection of the plane 3x – y + 2z – 4 = 0, x + y + z – 2 = 0 and the point (2, 2, 1) is

1) 7x + 5y + 4z + 8 = 0 2) 7x + 5y + 4z - 8 = 0 3) 7x - 5y + 4z - 8 = 0 4) None of these Solution: (3) 7x - 5y + 4z - 8 = 0... View Article

If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is

1) x + 2y + 4z = 12 2) 4x + 2y + z = 12 3) x + 2y + 4z = 3 4) 4x + 2y + z = 3 Solution: (2) 4x + 2y + z = 12... View Article

If the points (1, 2, 3) and (2, -1, 0) lie on the opposite sides of the plane 2x + 3y – 2z = k, then

1) k < 1 2) k > 2 3) k < 1 or k > 2 4) 1 < k < 2 Solution: (4) 1 < k < 2 Given, the points (1, 2, 3) and (2, -1, 0)... View Article

The point of intersection of the lines [x – 1] / 2 = [y – 2] / 3 = [z – 3] / 4 and [x – 4] / 5 = [y – 1] / 2 = z is

1) (0, 0, 0) 2) (1, 1, 1) 3) (-1, -1, -1) 4) (1, 2, 3) Solution: (3) (-1, -1, -1)... View Article

If the straight lines [x – 1] / k = [y – 2] / 2 = [z – 3] / 2 and [x – 2] / 3 = [y – 3] / k = [z – 1] / 3 intersect at a point, then the integer k =

1) -2 2) -5 3) 5 4) 2 Solution: (2) -5 The shortest distance between the two is 0.... View Article

If the line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ-plane at the point (0, 17 / 2, – 13 / 2), then

1) a = 8, b = 2 2) a = 2, b = 8 3) a = 4, b = 6 4) a = 6, b = 4 Solution: (4) a = 6, b = 4... View Article

Find the direction ratios of the line [3 – x] / 1 = [y – 2] / 5 = [2z – 3] / 1.

1) 1, 5, 1/2 2) -1, 5, 1 3) -1, 5, 1/2 4) 1, 5, 1 Solution: (3) -1, 5, 1/2 [3 - x] / 1 = [y - 2] / 5 = [2z - 3] / 1... View Article

If lines x = 1 + s, y = -3 – λs and x = t/2 , y = 1 + t , z = 2 – t, where s and t are parameters, are coplanar, then λ is equal to

1) -1/2 2) -1 3) -2 4) 0 Solution: (3) -2... View Article

M	T	W	T	F	S	S
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14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30

Archives

The image of the point (1, 3, 4) with respect to the plane 2x – y + z + 3 = 0 is

The plane ax + by + cz = 1 meets the coordinates axes at A, B and C. The centroid of ∆ABC is

A equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2, x – y + z = 3 and at a distance 2/√3 from the point (3, 1, -1), is

Foot of the perpendicular drawn from the origin to the plane 2x – 3y + 4z = 29 is

The image of the point with position vector i + 3k in the plane r. (i + j + k) = 1 is

The equation of the plane through the intersection of the plane 3x – y + 2z – 4 = 0, x + y + z – 2 = 0 and the point (2, 2, 1) is

If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is

If the points (1, 2, 3) and (2, -1, 0) lie on the opposite sides of the plane 2x + 3y – 2z = k, then

The point of intersection of the lines [x – 1] / 2 = [y – 2] / 3 = [z – 3] / 4 and [x – 4] / 5 = [y – 1] / 2 = z is

If the straight lines [x – 1] / k = [y – 2] / 2 = [z – 3] / 2 and [x – 2] / 3 = [y – 3] / k = [z – 1] / 3 intersect at a point, then the integer k =

If the line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ-plane at the point (0, 17 / 2, – 13 / 2), then

Find the direction ratios of the line [3 – x] / 1 = [y – 2] / 5 = [2z – 3] / 1.

If lines x = 1 + s, y = -3 – λs and x = t/2 , y = 1 + t , z = 2 – t, where s and t are parameters, are coplanar, then λ is equal to

The point of intersection [x – 5] / 3 = [y – 7] / – 1 = [z + 2] / 1 and [x + 3] / – 36 = [y – 3] / 2 = [z – 6] / 4 is

Lines [x – 2] / 1 = [y – 3] / 1 = [z – 4] / – k and [x – 1] / k = [y – 4] / 2 = [z – 5] / 1 are coplanar, if

Two lines [x – 1] / 2 = [y + 1] / 3 = [z – 1] / 4 and [x – 3] / 1 = [y – k] / 2 = z intersect at a point, if k =

What are the DR’s of vector parallel to (2, -1, 1) and (3, 4, -1)?

If OA is equally inclined to OX, OY and OZ and if A is √3 units from the origin, then A is

If a line makes angles α, β and γ with the coordinate axes, then

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