Arts (English Medium) Class 12 - CBSE Question Bank Solutions

Find the sine of the angle between the vectors `vec"a" = 3hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" - 2hat"j" + 4hat"k"`.

The value of sin `["cos"^-1 (7/25)]` is ____________.

If A, B, C, D are the points with position vectors `hat"i" + hat"j" - hat"k", 2hat"i" - hat"j" + 3hat"k", 2hat"i" - 3hat"k", 3hat"i" - 2hat"j" + hat"k"`, respectively, find the projection of `vec"AB"` along `vec"CD"`.

The value of tan `("cos"^-1  4/5 + "tan"^-1  2/3) =`

The equation sin^-1 x – cos^-1 x = cos^-1 `(sqrt3/2)` has ____________.

Find the minor of the element of the second row and third column in the following determinant `[(2,-3,5),(6,0,4),(1,5,-7)]`

If `Delta = abs((5,3,8),(2,0,1),(1,2,3)),` then write the minor of the element a₂₃.

Position vector of a point P is a vector whose initial point is origin.

If `"abc" ne 0  "and" abs ((1 + "a", 1, 1),(1, 1 + "b", 1),(1,1,1 + "c")) = 0, "then"  1/"a" + 1/"b" + 1/"c" =` ____________.

If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.

Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).

If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.

The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.

P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.

If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.

A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.

If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.

If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin²α + sin²β + sin²γ is ______.

If a line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis is ______.

The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`