All the points on the x-axis have 1) x = 0 2) y = 0 3) x = 0, y = 0 4) y = 0, z = 0 Solution: (4) y = 0, z = 0 It is a fundamental concept.... View Article
The direction cosines of a line equally inclined to all the three rectangular co-ordinate axis are 1) √3, √3, √3 2) 1 / √3, 1 / √3, 1 / √3 3) 1, 1, 1 4) None of these Solution: (2) 1 / √3, 1 / √3, 1 / √3... View Article
The triangle formed by the points (0, 7,10), (–1, 6, 6), (–4, 9, 6) is 1) Equilateral 2) Isosceles 3) Right-angled 4) Right-angled isosceles Solution: (4) Right-angled isosceles... View Article
If the points (–1, 2, – 3), (4, a, 1) and (b, 8, 5) are collinear, then a and b are respectively equal to 1) 5 and 5 2) 9 and 5 3) 5 and 9 4) –5 and 9 Solution: (3) 5 and 9... View Article
A vector perpendicular to the plane containing the points A (1, -1, 2), B (2, 0, -1) and C (0, 2, 1) is 1) 4i + 8j - 4k 2) 8i + 4j + 4k 3) 3i + j + 2k 4) i + j - k Solution: (2) 8i + 4j + 4k... View Article
If P (3, 2, 6) is a point in space and Q is a point on the line r = (i – j + 2k) + (- 3i + j + 5k). Then the value of for which the vector PQ is parallel to the plane x – 4y + 3z = 1 is 1) 1/4 2) - (1/4) 3) 1/8 4) -(1/8) Solution: (1) ¼... View Article
Find the distance between the planes r . (2i + j + 3k) and r . (6i – 3j + 9k) + 13 = 0. 1) 5 / 3√14 2) 10 / 3√14 3) 25 / 3√14 4) None of these Solution: (3) 25 / 3√14... View Article
The angle between the line r = (i + 2j + 3k) + λ (2i + 3j + 4k) and the plane r . (i + 2j – 2k) = 0 is 1) 0o 2) 60o 3) 30o 4) 90o 5) 45o Solution: (1) 0o... View Article
The distance between the line vector r = 2i – 2j + 3k + λ (i – j + 4k) and the plane vector r (i + 5j + k) = 5 is 1) 10 / 3√3 2) 10 / 9 3) 10 / 3 4) 3 / 10 Solution: (1) 10 / 3√3... View Article
Find the angle between the lines vector r = (2i – 3j + k) + l (i + j + 3k) and vector = (i – j – k) + μ (2i – 3j + k) 1) π / 2 2) cos-1 (9 / √91) 3) cos-1 (2 / √154) 4) π / 3 Solution: (3) cos-1 (2 / √154)... View Article
The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius 1) √2 2) 2 3) 1 4) 3 Solution: (3) 1... View Article
If (2, 3, 5) is one end of a diameter of the sphere x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0, then the coordinates of the other end of the diameter are 1) (4, 9, -3) 2) (4, -3, 3) 3) (4, 3, 5) 4) (4, 3, -3) Solution: (1) (4, 9, -3)... View Article
The radius of the sphere x2 + y2 + z2 = x + 2y + 3z is 1) √14/2 2) √7 3) 7/2 4) √7/2 Solution: (1) √14/2... View Article
The shortest distance from the point (1, 2, -1) to the surface of the sphere x2 + y2 + z2 = 54 is 1) 3√6 2) 2√6 3) √6 4) 2 Solution: (2) 2√6 The equation of sphere is x2 + y2 + z2 = 54. The centre and radius of this sphere are... View Article
The intersection of the spheres x2 + y2 + z2 + 7x – 2y – z = 1 and x2 + y2 + z2 – 3x + 3y + 4z = – 4 is same as the intersection of one of the spheres and the plane is 1) 2x - y - z = 1 2) -2x + y + z = 1 3) 2x - y + z = 1 4) 2x = y + z = 1 Solution: (1) 2x - y - z = 1... View Article
The equation of a sphere having centre (- 1, 2, – 3) and radius 3 units is 1) x2 + y2 + z2 - 2x - 4y - 6z = 0 2) x2 + y2 + z2 + 2x - 4y + 6z + 5 = 0 3) x2 + y2 + z2 - 2x - 4y - 6z - 5 = 0 4) None of these... View Article
The line perpendicular to the plane 2x – y + 5z = 4 passing through the point (-1, 0, 1) is 1) [x + 1] / 2 = - y = [z - 1] / - 5 2) [x + 1] / - 2 = y = [z - 1] / - 5 3) [x + 1] / 2 = - y = [z - 1] / 5 4) [x + 1] / 2 = y = [z -... View Article
The equation of the plane containing the line [x – x1] / l = [y – y1] / m = [z – z1] / n is 1) ax1 + by1 + cz1 = 0 2) al + bm + cn = 0 3) (a / l) = (b / m) = (c / n) 4) lx1 + my1 + nz1 = 0 Solution: (2) al + bm + cn = 0... View Article
If the plane 2x – y + z = 0 is parallel to the line [2x – 1] / 2 = [2 – y] / 2 = [z + 1] / a, then the value of a is 1) 4 2) - 4 3) 2 4) - 2 5) 0 Solution: (2) - 4 The given line is [x - (1 / 2)] / 1 = [y - 2] / - 2 = [z - (- 1)] / a. The... View Article
The equation of the plane passing through the origin and containing the line [x – 1] / 5 = [y – 2] / 4 and [z – 3] / 5 is 1) x + 5y - 3z = 0 2) x - 5y + 3z = 0 3) x - 5y + 3z = 0 4) 3x - 10y + 5z = 0 5) x + 5y + 3z = 0 Solution: (2) x - 5y + 3z = 0... View Article
