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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... 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,... 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. \(\begin{array}{l}\begin{array}{l}... 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 =... 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,... 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 \(\begin{array}{l}\begin{array}{l} \frac{x-1}{1}-\frac{y+3}{-\lambda}=\frac{z-1}{\lambda} \& \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{-2}\\ \text { For Co- }... 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,... 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 =... 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 \(\begin{array}{l}\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}=r\\ x=2 r+1, y=3 r-1, z=4 r+1\\ \text \... 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,... View Article

If OA is equally inclined to OX, OY and OZ and if A is √3 units from the origin, then A is

1) (3, 3, 3) 2) (-1, 1, -1) 3) (-1, 1,1) 4) (1, 1, 1) Solution: (4) (1, 1, 1)... View Article

If a line makes angles α, β and γ with the coordinate axes, then

1) cos 2α + cos 2β + cos 2γ – 1 = 0 2) cos 2α + cos 2β +... View Article

If a line in the space makes angles α, β and γ with the coordinates axes, the cos 2α + cos 2β + cos 2γ + sin² α + sin² β + sin² γ equals

1) -1 2) 0 3) 1 4) 2 Solution: (3) 1 \(\begin{array}{l}\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+\sin ^{2} \alpha+\sin... View Article

The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

1) 3 2) 2 3) 2√2 4) 3√2 Solution: (4) 3√2 \(\begin{array}{l}\begin{array}{l} A B=\sqrt{(0-1)^{2}+(1-0)^{2}+0^{2}}=\sqrt{2}\\ B C=\sqrt{0^{2}+(0-1)^{2}+(1-0)^{2}}=\sqrt{2}\\ C A=\sqrt{(1-0)^{2}+0^{2}+(0-1)^{2}}=\sqrt{2}\\ \therefore \text... View Article