﻿ Important Questions of Vector Algebra Mathematics | Zigya

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## Mathematics : Vector Algebra

#### Multiple Choice Questions

481.

If three numbers are drawn at random successively without replacement from a set S = {1, 2, ... 10}, then the probability that the minimum of the chosen numbers is 3 or their maximum is 7

• $\frac{11}{40}$

• $\frac{5}{40}$

• $\frac{3}{40}$

• $\frac{1}{40}$

482.

• 8

•  - 8

• $\frac{146}{17}$

483.

If a, b and c are non-zero vectors such that a and b are not perpendicular to each other, then the vector r which is perpendicular to a and satisfying r x b = c x b  is

484.

• (- 2, 5, 3)

• (2, - 5, 3)

• (2, 5, 3)

• (2, 5, - 3)

485.

If the volume of the tetrahedron formed by the coterminous edges a, b and c is 4, then the volume of the parallelopiped formed by the coterminous edges a x b, b x c and c x a is

• 576

• 48

• 16

• 144

486.

487.

Let the position vectors of points 'A' and 'B' be , respectively. A point 'P' divides the line segment AB internally in the ratio $\mathrm{\lambda }$ : 1 ($\mathrm{\lambda }$ > 0). If O is the origin and  then $\mathrm{\lambda }$ is equal to

#### Multiple Choice Questions

488.

• 0

• $\frac{2\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{9}$

489.

Let x0 be the point of local maxima of

is :

• - 22

• 14

•  - 4

•  - 30

490.

Suppose the vectors x1, x2 and x3 are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b1, b2 and b3 respectively. If

,

then the determinant of A is equal of A is

• $\frac{3}{2}$

• 4

• $\frac{1}{2}$

• 2