The equation of the plane that contains the point A (1, -1, 2) and is perpendicular to each of the planes 2x + 3y – 2z = 5 and x + 2y – 3z = 8 is 1) 5x + 4y - z = 7 2) 5x - 4y + z = 7 3) -5x + 4y - z = 7 4) 5x - 4y - z = 7 Solution: (4) 5x - 4y - z = 7... View Article
An equation of the plane through the points (1, 0, 0), (0, 2, 0) and at a distance 6/7 units from the origin, is 1) 6x + 3y + z - 6 = 0 2) 6x + 3y + 2z - 6 = 0 3) 6x + 3y + z + 6 = 0 4) 6x + 3y + 2z + 6 = 0 5) 6x + 2y + 3z + 6 = 0 Solution:... View Article
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
The point of intersection [x – 5] / 3 = [y – 7] / – 1 = [z + 2] / 1 and [x + 3] / – 36 = [y – 3] / 2 = [z – 6] / 4 is 1) (5, 7, -2) 2) (-3, 3, 6) 3) (2, 10, 4) 4) (21, 5/3, 10/3) Solution: (4) (21, 5/3, 10/3)... View Article
Lines [x – 2] / 1 = [y – 3] / 1 = [z – 4] / – k and [x – 1] / k = [y – 4] / 2 = [z – 5] / 1 are coplanar, if 1) k = 2 2) k = 0 3) k = 3 4) k = -1 Solution: (2) k = 0... View Article
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 = 1) 2/9 2) 1/2 3) 9/2 4) 1/6 Solution: (3) 9/2... View Article
What are the DR’s of vector parallel to (2, -1, 1) and (3, 4, -1)? 1) (1, 5, -2) 2) (-2, -5, 2) 3) (-1, 5, 2) 4) (-1, -5, -2) Solution: (1) (1, 5, -2)... View Article