The coordinate of the point of intersection of the line [x – 1] / 1 = [y + 2] / 3 = [z – 2] / – 2 with the plane 3x + 4y + 5z – 25 = 0 is 1) (5, 10, 6) 2) (10, 5, 6) 3) (5, 5, -6) 4) (5, 10, -6) Solution: (4) (5, 10, -6) [x - 1] / 1 = [y + 2] / 3 = [z - 2] / - 2 = r... View Article
The distance of origin from the point of intersection of the line (x / 2) = [y – 2] / 3 = [z – 3] / 4 and the plane 2x + y – z = 2 is 1) √120 2) √83 3) 2√19 4) √78 Solution: (4) √78... View Article
The angle between the line [x – 1] / 2 = [y – 2] / 1 = [z + 3] / – 2 and the plane x + y + 4 = 0 is 1) 0o 2) 30o 3) 45o 4) 90o Solution: (3) 45o... View Article
If the line [x – 2] / 3 = [y – 1] / – 5 = [z + 2] / 2 lies on the plane x + 3y – É‘, z + β = 0, then (É‘, β) = 1) (6, -17) 2) (- 6, 7) 3) (5, -15) 4) (-5, 15) Solution: (2) (- 6, 7) Direction ratios of the line (3, - 5, 2) Direction ratios... View Article
The distance of the point (3, 8, 2) from the line [x – 1] / 2 = [y – 3] / 4 = [z – 2] / 3 measured parallel to the plane 3x + 2y – 2z = 0 is 1) 2 2) 3 3) 6 4) 7 Solution: (4) 7... View Article
The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, -1, 4) with the plane 5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR, then the length of the line segment PS is 1) 1/√2 2) √2 3) 2 4) 2√2 Solution: (1) 1/√2 The direction ratios of QR is 1, 4, 1. The coordinate of P = (4 / 3, 1 / 3, 13... View Article
A plane which passes through the point (3, 2, 0) and the line (x – 4)/1 = (y – 7)/5 = (z – 4)/4 is 1) x - y + z = 1 2) x + y + z = 5 3) x + 2y - z = 0 4) 2x - y + z = 5 Solution: (1) x - y + z = 1 It is given that the point (3, 2, 0) lies... View Article
The line [x – 2] / 3 = [y – 3] / 4 = [z – 4] / 5 is parallel to the plane 1) 3x + 4y + 5z = 7 2) 2x + 3y + 4z = 0 3) x + y - z = 2 4) 2x + y - 2z = 0 Solution: (4) 2x + y - 2z = 0 Since 3 (2) + 4 (1) + 5... View Article
Equation of the plane perpendicular to the line (x / 1) = (y / 2) = (z / 3) and passing through the point (2, 3, 4) is 1) 2x + 3y + z = 17 2) x + 2y + 3z = 9 3) 3x + 2y + z = 16 4) x + 2y + 3z = 20 Solution: (4) x + 2y + 3z = 20... View Article
The line joining points (1, 1, 2) and (3, -2, 1) meets the plane 3x + 2y + z = 6 at the point 1) (1, 1, 2) 2) (3, -2, 1) 3) (2, -3, 1) 4) (3, 2, 1) Solution: (2) (3, -2, 1)... View Article
If the planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line, then a2 + b2 + c2 + 2abc is 1) 0 2) 1 3) 2 4) 3 Solution: (2) 1... View Article
The distance of the plane 6x – 3y + 2z + 14 = 0 from the origin is 1) 2 2) 1 3) 14 4) 8 Solution: (1) 2... View Article
The intercepts of the plane 2x – 3y + 4z = 12 on the coordinate axes are given by 1) 3, -2, 15 2) 6, -4, 3 3) 6, -4, -3 4) 2, -3, 4 Solution: (2) 6, -4, 3 The general equation of a plane is given by, Ax + By + Cz... View Article
A plane makes intercepts a, b, c at A, B, C on the coordinates axes, respectively. If the centroid of ∆ABC is at (3, 2, 1), then the equation of the plane is 1) x + 2y + 3z = 9 2) 2x - 3y - 6z = 18 3) 2x + 3y + 6z = 18 4) 2x + y + 6z = 18 5) 2x + 3y + 6z = 9 Solution: (3) 2x + 3y + 6z = 18... View Article
Equation of the plane passing through the intersection of the planes x + y + z = 6, 2x + 3y + 4z + 5 = 0 and the point (1, 1, 1) is 1) 20x + 23y + 26z - 69 = 0 2) 31x + 45y + 49z + 52 = 0 3) 8x + 5y + 2z - 69 = 0 4) 4x + 5y + 6z - 7 = 0 Solution: (1) 20x + 23y + 26z - 69 = 0... View Article
Statement I: The point A(3, 1, 6) is the mirror image of the point P(1, 3, 4) in the plane x – y + z = 5. Statement II: The plane x – y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). 1) Statement I is correct, Statement II is correct; Statement II is the correct explanation for Statement I 2) Statement I is correct,... View Article
If the distance of the point P(1, -2, 1) from the plane x + 2y – 2z = alpha, where alpha > 0, is 5, then the foot of the perpendicular from P to the plane is 1) (8 / 3, 4 / 3, - 7 / 3) 2) (4 / 3, - 4 / 3, 1 / 3) 3) (1 / 3, 2 / 3, 10 / 3) 4) (2 / 3, - 1 / 3, 5 / 2) Solution: (1) (8 / 3, 4 / 3, - 7 /... View Article
The equation of the plane perpendicular to Z – axis and passing through (2, -3, 5) is 1) x - 2 = 0 2) y + 3 = 0 3) z - 5 = 0 4) 2x - 3y + 5z + 4 = 0 Solution: (3) z - 5 = 0 The plane is perpendicular to the z-axis... View Article
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
