Important Questions of Vector Algebra Mathematics | Zigya

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

Advertisement
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 r = αb × c + βc × a + γa × b and [a b c] = 2, then α + β + γ is equal to

  • r . b × c + c × a + a × b

  • 12r . a +b + c

  • 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

  • 32(i + j)

  • 23(i + J)

  • 12(i + j)

  • 13(i + j)


Advertisement
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

  • 46 sq units

  • 1221 sq units

  • 62 sq units

  • 6 sq units


56.

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

  • 5610

  • 199

  • 919

  • 619


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 a = 2i^ + 2j^ + 3k^b = - i^ + 2j^ + k^ and c = 3i^ + j^ then a + tb is perpendicular to c, if t is equal to

  • 2

  • 4

  • 6

  • 8


Advertisement
59.

The distance between the line r = 2i^ - 2j^ + 3k^ + λi^ - j^ + 4k^ and the plane r .  i^ + 5j^ + k^ = 5, is

  • 103

  • 103

  • 1033

  • 109


60.

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

a1 = 2i^ - j^ + k^, a2 = 3i^ - 4j^ - 4k^,a3 = i^ + j^ - k^ and a4 = - i^ + 3j^ + k^,

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


Advertisement