﻿ Important Questions of Vector Algebra Mathematics | Zigya

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## Mathematics : Vector Algebra

#### Multiple Choice Questions

51.

For any three vectors a, b and c [a + b, b + c, c + a] is

• [a, b, c]

• 3[a, b, c]

• 2[a, b, c]

• 0

52.

If  and [a b c] = 2, then  is equal to

• 2r . (a + b + c)

• 4

53.

If a, b, c are three non-coplanar vectors and p, q, rare reciprocal vectors, then (la + mb + nc) · (lp + mq + nr) is equal to

• l + m + n

• l3 + m3 + n3

• l2 + m2 + n2

• None of these

54.

The vector b = 3j + 4k is to be written as the sum of a vector b1 parallel to a = i + j and a vector b2 perpendicular to a. Then, b1 is equal to

• $\frac{3}{2}$(i + j)

• $\frac{2}{3}$(i + J)

• $\frac{1}{2}$(i + j)

• $\frac{1}{3}$(i + j)

55.

If a = i + j + k, b = i + 3j + 5k and c = 7i + 9j + 11k, then the area of parallelogram having diagonals a + b and  b + c is

• 4$\sqrt{6}$ sq units

• $\frac{1}{2}\sqrt{21}$ sq units

• $\frac{\sqrt{6}}{2}$ sq units

• $\sqrt{6}$ sq units

56.

The projection of the vector i - 2j + k on the vector 4i - 4j + 7k is

• $\frac{5\sqrt{6}}{10}$

• $\frac{19}{9}$

• $\frac{9}{19}$

• $\frac{\sqrt{6}}{19}$

57.

If a, b, c are three non-zero vectors such that a + b+ c = 0 and m = a . b + b . c + c · a, then

• m < 0

• m > 0

• m = 0

• m = 3

58.

If  and  then  is perpendicular to c, if t is equal to

• 2

• 4

• 6

• 8

59.

The distance between the line  and the plane , is

• $\frac{10}{3}$

• $\frac{10}{\sqrt{3}}$

• $\frac{10}{3\sqrt{3}}$

• $\frac{10}{9}$

60.

If m1, m2, m3 and m4 are respectively the magnitudes of the vectors

then the correct order of m1, m2, m3 and m4 is

• m3 < m1 < m4 < m2

• m3 < m1 < m2 < m4

• m3 < m4 < m1 < m2

• m3 < m4 < m2 < m1