Home
Class 12
MATHS
Let vecu = u(1)hati + u(2)hatj +u(3)hat...

Let ` vecu = u_(1)hati + u_(2)hatj +u_(3)hatk` be a unit vector in ` R^(3) and vecw = 1/sqrt6 ( hati + hatj + 2hatk)` , Given that there exists a vector `vecv " in " R^(3)` such that ` | vecu xx vecv| =1 and vecw . ( vecu xx vecv) =1` which of the following statements is correct ?

A

there is exactly one choice for such `vecv`

B

There are infinintely many choices for such `vecv`

C

if `vecu` lies in the xy-plane then `|u_(1)|=|u_(2)|`

D

If `vecu` lies in the xy-plane then `2|u_(1)|=|u_(3)|`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Similar Questions

Explore conceptually related problems

Let vecu = u_(1) hati + u_(2) hatj be a unit vector in xy plane and vecw = 1/sqrt6 (hati +hatj +2hatk) . Given that there exists a vector vecc " in " R_(3) " such that |vecu xx vecv|=1 and vecw . (vecu xx vecv) =1 , then

Let vecu=u_(1)hati +u_(3)hatk be a unit vector in xz-plane and vecq = 1/sqrt6 ( hati + hatj + 2hatk) . If there exists a vector vecv in such that |vecu xx vecu|=1 and vecw . (vecu xx vecc) .Then

Let vecu and vecv be unit vectors such that vecu xx vecv + vecu = vecw and vecw xx vecu = vecv . Find the value of [vecu vecv vecw ]

Let vecu = 2hati - hatj + hatk, vecv = -3hatj + 2hatk be vectors in R^(3) and vecw be a unit vector in the xy-plane. Then the maximum possible value of |(vecu xx vecv).vecw| is-

The figure given below shows the orientation of two vectors vecu and vecv in the xy plane . if vecu=ahati+b hatj and vecv=phati+qhatj Which of the following is correct ?

Figure shows the orientation of two vectors u and v in the XY plane. if vecu=ahati+bhatj and vecv=p hati+qhatj which of the following is correct?

The unit vector parallel to the resultant vector of 2hati+4hatj-5hatk and hati+2hatj+3hatk is

For three vectors, vecu, vecv and vecw which of the following expressions is not equal to any of the remaining three ?

Let vecu= hati + hatj , vecv = hati -hatja and hati -hatj and vecw =hati + 2hatj + 3 hatk If hatn isa unit vector such that vecu .hatn=0 and vecn .hatn =0 , " then " |vecw.hatn| is equal to