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 /... View Article
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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... 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 \(\begin{array}{l}\text \ Centre \ of \ sphere \ is... 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,... 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 \(\begin{array}{l}\begin{array}{l} \text { Given equation of sphere is }... 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 +... 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... 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... 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]... 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)... 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... 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... View Article
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,... 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 \(\begin{array}{l}\begin{array}{l} (x, y, z)\\ =(2 \lambda, 3 \lambda+2,4 \lambda+3)\\... 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 \(\begin{array}{l}\text \ The \ angle \ between \ the... View Article
If the line [x – 2] / 3 = [y – 1] / – 5 = [z + 2] / 2 lies on the plane x + 3y – ɑ, z + β = 0, then (ɑ, β) =
1) (6, -17) 2) (- 6, 7) 3) (5, -15) 4) (-5, 15) Solution: (2) (- 6, 7) 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 \(\begin{array}{l}\text \ Equation \ of \ plane\\ 3 x+2... 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.... 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... 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... View Article
