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
21.

A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is

  • 90°

  • 120°

  • 45°

  • 45°

114 Views

22.

The values of a, for which the points A, B, C with position vectors 2 straight i with hat on top minus straight j with hat on top plus straight k with hat on top comma space straight i with hat on top minus 3 straight j with hat on top minus 5 straight k with hat on top space and space straight a straight i with hat on top minus 3 straight j with hat on top plus straight k with hat on toprespectively are the vertices of a right-angled triangle with C =π/2  are

  • 2 and 1

  • −2 and −1

  • −2 and 1

  • −2 and 1

102 Views

23.

ABC is a triangle. Forces straight P with rightwards arrow on top comma space straight Q with rightwards arrow on top comma space straight R with rightwards arrow on top space acting along IA, IB and IC respectively are in equilibrium, where I is incentre of ∆ABC. Then P : Q : R is

  • sin A : sin B : sin C

  • sin space straight A over 2 space colon space Sin space straight B over 2 space colon space sin space straight C over 2
  • cos space straight A over 2 colon space cos space straight B over 2 space colon space Cos space straight C over 2
  • cos space straight A over 2 colon space cos space straight B over 2 space colon space Cos space straight C over 2
201 Views

24.

If C is the mid -point of AB and P is any point outside AB, then

  • PA with rightwards arrow on top space plus space PB with rightwards arrow on top space equals space 2 PC with rightwards arrow on top
  • PA with rightwards arrow on top space plus space PB with rightwards arrow on top space equals space PC with rightwards arrow on top
  • PA with rightwards arrow on top space plus space PB with rightwards arrow on top space plus space 2 PC with rightwards arrow on top space equals space 0
  • PA with rightwards arrow on top space plus space PB with rightwards arrow on top space plus space 2 PC with rightwards arrow on top space equals space 0
129 Views

Advertisement
25.

For any vector straight a with rightwards arrow on top  the value of left parenthesis straight a with rightwards arrow on top space straight x straight i with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight j with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight k with hat on top right parenthesis squared is equal to

  • 3 straight a with rightwards arrow on top squared
  • straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared
119 Views

26.

Let a, b and c be distinct non-negative numbers. If the vectors straight a straight i with hat on top space plus straight a space straight j with hat on top space plus space straight c straight k with hat on top comma space space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space 

  • the Geometric Mean of a and b

  • the Arithmetic Mean of a and b

  • equal to zero

  • equal to zero

117 Views

27.

If straight a with rightwards arrow on top comma straight b with rightwards arrow on top comma space straight c with rightwards arrow on top are non -coplanar vector λ is a real number then

open square brackets straight lambda left parenthesis straight a with rightwards arrow on top space plus straight b with rightwards arrow on top right parenthesis space straight lambda squared space straight b with rightwards arrow on top straight lambda space straight c with rightwards arrow on top close square brackets space equals space open square brackets straight a with rightwards arrow on top space straight b with rightwards arrow on top space plus straight c with rightwards arrow on top straight b with rightwards arrow on top close square brackets space for

  • exactly one value of λ

  • no value of λ

  • exactly three values of λ

  • exactly three values of λ

261 Views

28. Let space straight a with rightwards arrow on top space equals space straight i with hat on top space minus straight k with hat on top comma space straight b with rightwards arrow on top space equals space straight x straight i with hat on top space plus straight j with hat on top space plus left parenthesis 1 minus straight x right parenthesis space straight k with hat on top space and space
straight c with rightwards arrow on top space equals space straight y straight i with hat on top space plus straight x space straight j with hat on top space plus left parenthesis 1 plus straight x minus straight y right parenthesis straight k with hat on top space. Then space left square bracket straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top right square bracket depends on
  • only y

  • only x

  • both x and y

  • both x and y

99 Views

Advertisement
29.

The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is 

  • 2 : 1

  • 3 colon square root of 2
  • 3:2

  • 3:2

127 Views

30.

Let straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top be three non-zero vectors such that no two of these are collinear. If the vector straight a with rightwards arrow on top space plus 2 straight b with rightwards arrow on top is collinear withstraight c with rightwards arrow on top space and space straight b with rightwards arrow on top space plus 3 straight c with rightwards arrow on top is collinear with straight a with rightwards arrow on top (λ being some non-zero scalar) then straight a with rightwards arrow on top space plus 2 straight b with rightwards arrow on top space plus 6 straight c with rightwards arrow on top equals

  • λstraight a with rightwards arrow on top

  • λstraight b with rightwards arrow on top

  • λstraight c with rightwards arrow on top

  • λstraight c with rightwards arrow on top

147 Views

Advertisement