1) 30° 2) 45° 3) 60° 4) 75° Solution: (3) 60° \(\begin{array}{l}\begin{array}{l} \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\... View Article

If a line makes angles ɑ, β, , with four diagonals of a cube, then the value of sin² ɑ + sin² β + sin² + sin² is

1) 4 / 3 2) 1 3) 8 / 3 4) 7 / 3 Solution: (3) 8 / 3 \(\begin{array}{l}\text... View Article

Points (-2, 4, 7), (3, – 6, – 8) and (1, – 2, – 2) are

1) Collinear 2) Vertices of an equilateral triangle 3) Vertices of an isosceles triangle 4) None of the above Solution:... View Article

A line makes angles α, β, γ with the co-ordinate axis. If α + β = 90°, then γ =

1) 0 2) 90° 3) 180° 4) None of these Solution: (2) 90° \(\begin{array}{l}\begin{array}{l} \cos ^{2} \alpha+\cos ^{2}\left(90^{\circ}-\alpha\right)+\cos ^{2} \gamma=1... View Article

The co-ordinates of the point P are (x, y, z) and the direction cosines of the line OP when O is the origin, are l, m, n. If OP = r, then

1) l = x, m = y, n = z 2) l = xr, m = yr, n = zr... View Article

If the coordinates of A and B be (1, 2, 3) and (7, 8, 7), then the projections of the line segment AB on the co-ordinate axis are

1) 6, 6, 4 2) 4, 6, 4 3) 3, 3, 2 4) 2, 3, 2 Solution: (1) 6, 6,... View Article

The point of intersection of the line joining the points (3, 4, 1) and (5, 1, 6) and the xy-plane is

1) (13, 23, 0) 2) (13 / 5, 23 / 5, 0) 3) (- 13, 23, 0) 4) (- 13... View Article

If A (1, 2, – 1) and B (-1, 0, 1) are given, then the co-ordinates of P which divides AB externally in the ratio 1: 2 are

1) (1 / 3) (1, 4, – 1) 2) (3, 4, – 3) 3) (1 / 3) (3, 4, –... View Article

«
1
…
2,830
2,831
2,832
2,833
2,834
…
5,472
»

Latest Posts

If a line makes α, β, γ, δ angles with four diagonals of a cube, then cos² α + cos² β + cos² γ + cos² δ =

If a line makes angles α, β, γ with the co-ordinate axis, then

The points (5, – 4, 2), (4, – 3, 1), (7, – 6, 4) and (8, – 7, 5) are the vertices of

The projection of the line segment joining the points (-1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3 is

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1, -1, 2) and (2, 1, -1) are

The coordinates of the point in which the line joining the points (3, 5, – 7) and (-2, 1, 8) is intersected by the plane yz are given by

The direction ratios of the line joining the points (4, 3, – 5) and (-2, 1, – 8) are

If (1 / 2, 1 / 3, n) are the direction cosines of a line, then the value of n is

If the projection of any line on co-ordinate axis 3, 4, and 5, then its length is

A line AB in three-dimensional space makes angle 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals