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... View Article
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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,... 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 \(\begin{array}{l}\mathrm{x}-\mathrm{cy}-\mathrm{bz}=0 \ldots \ldots (1)\\ \mathrm{Cx}-\mathrm{y}+\mathrm{az}=0 \ldots \ldots (2)\\ b... 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 \(\begin{array}{l}\begin{array}{l} \text { Distance of a plane } \mathrm{ax}+\mathrm{by}+\mathrm{cz}+\mathrm{d}=0... 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,... 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... 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... 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... 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... 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... 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... 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... 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,... 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 /... 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... 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... 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)... 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)... 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... 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... View Article
