Home
Class 12
MATHS
If veca=hati+hatj+hatk, veca.vecb=1 and ...

If `veca=hati+hatj+hatk, veca.vecb=1` and `vecaxxvecb=hatj-hatk` then `vecb`

A

3

B

9

C

10

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
Let `vecb=alphahati+betahatj+lambdahatk, veca xx vecb=hatj-hatk`
`rArr |{:(hati,hatj,hatk),(1,1,1),(alpha,beta,lambda):}|=hatj-hatk`
`rArr beta-lambda=0, alpha-lambda=1,alpha-beta=1`
`rArr beta=lambda,alpha=1+lambda,alpha=1+beta`
`veca.vecb=1`
`rArr alpha+beta+lambda=1, rArr beta+1+beta+beta =1 rArr beta=0`
`therefore alpha=1, lambda=0, therefore vecb=hati`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

Similar Questions

Explore conceptually related problems

If veca=2hati+hatj-hatk, vecb= -hati+2hatj+hatk, vecc=-hati+2hatj-hatk then the unit vector perpendicular to both veca+vecb and vecb +vec c is :

A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk,vecb=2hati+hatj and vecc=3hatj-2hatk. Let vecx,vecy and vecz be three vectors in the plane of veca,vecb;vecb,vec;vecc,veca, respectively. Then

A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk,vecb=2hati+hatj and vecc=3hatj-2hatk. Let vecx,vecy and vecz be three vectors in the plane of veca,vecb;vecb,vec;vecc,veca, respectively. Then

If veca=3hati-2hatj+hatk and vecb=2hati-4hatj+hatk then find |veca-2vecb|.

Given veca = 2hati + hatj - 8 hatk and vecb = hati + 3hatj - 4hatk then |veca + vecb| = ……………………… .

Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hatk be three vectors . A vector in the pland of vecb and vecc whose projection on veca is of magnitude sqrt((2/3)) is (A) 2hati+3hatj+3hatk (B) 2hati+3hatj-3hatk (C) -2hati-hatj+5hatk (D) 2hati+hatj+5hatk

If veca=hati+hatj+hatk and vecb = hati-2hatj+hatk then find vector vecc such that veca.vecc = 2 and veca xx vecc = vecb

Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj - hatk be three vectors. A vectors vecv in the plane of veca and vecb , whose projection on vecc is 1/sqrt3 is given by

If veca=-3hati-hatj+5hatk , vecb=hati-2hatj+hatK , vecc=4hatj-5hatk , find veca.(vecbxxvecc) .