Home
Class 12
MATHS
If non-zero vectors veca and vecb are eq...

If non-zero vectors `veca and vecb` are equally inclined to coplanar vector `vecc`, then `vecc` can be

A

`(|veca|)/(|veca|+2|vecb|)veca + (|vecb|)/(|veca| + |vecb|) vecb`

B

`(|vecb|)/(|veca| + |vecb|) veca + (|veca|)/(|veca|+ |vecb|) vecb`

C

`(|veca|)/(|veca|+2|vecb|)veca + (|vecb|)/(|veca|+ 2|vecb|)vecb`

D

`(|vecb|)/(2|veca| + |vecb|) veca + (|veca|)/(2|veca|+ |vecb|) vecb`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Since `veca and vecb` are equally inclined to `vecc, vecc` must be of the form `t((veca )/(|veca|)+ (vecb)/(|vecb|))`.
Now `(|vecb|)/(|veca | + |vecb|) veca + (|veca|)/(|veca| + |vecb|) vecb`
`" " = (|veca||vecb|)/(|veca| + |vecb|) ((veca)/(|veca|)+ (vecb)/(|vecb|))`
Also, `(|vecb|)/(2|veca|+ |vecb|) veca + (|veca|)/(2|veca|+|vecb|) vecb`
`" "= (|veca||vecb|)/(2|veca|+ |vecb|)((veca)/(|veca|)+ (vecb)/(|vecb|))`
Other two vectors cannot be written in the form
`t((veca)/(|veca|)+ (vecb)/(|vecb|))`.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Reasoning Questions)|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Comprehension)|9 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Single)|34 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise All Questions|529 Videos

Similar Questions

Explore conceptually related problems

The non zero vectors veca,vecb, and vecc are related byi veca=8vecb nd vecc=-7vecb. Then the angle between veca and vecc is (A) pi (B) 0 (C) pi/4 (D) pi/2

Vectors veca, vecb, vecc are three unit vectors and vecc is equally inclined to both veca and vecb . Let veca xx (vecb xx vecc) + vecb xx (vecc xx veca) =(4+x^(2))vecb-(4xcos^(2)theta)veca , then veca and vecb are non-collinear vectors, x gt 0

Given three vectors veca, vecb and vecc are non-zero and non-coplanar vectors. Then which of the following are coplanar.

Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr.vecc =0 for given non- zero vectors veca vecb and vecc Statement 1: [ veca - vecb vecb - vecc vecc- veca] =0 Statement 2: [veca vecb vecc] =0

If veca, vecb and vecc are unit coplanar vectors , then the scalar triple porduct [2 veca -vecb" " 2vecb - vecc " "2vecc-veca] is

If veca, vecb and vecc 1 are three non-coplanar vectors, then (veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)] equals

If veca, vecb and vecc are three non-zero, non-coplanar vectors,then find the linear relation between the following four vectors : veca-2vecb+3vecc, 2veca-3vecb+4vecc, 3veca-4vecb+ 5vecc, 7veca-11vecb+15vecc .

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc0 is (A) |[veca vecb vecc]| (B) |vecr| (C) |[veca vecb vecr]vecr| (D) none of these

If vectors, vecb, vcec and vecd are not coplanar, the pove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecxxvecb),(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)= (A) [veca vecb vecc] (B) 2[veca vecb vecc]vecr (C) 3[veca vecb vecc]vecr (D) 4[veca vecb vecc]vecr