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Sneha Chanda
Asked: 2022-11-02T01:14:50+05:30 In:

Let `veca=hati + 2hatj +hatk, vecb=hati – hatj +hatk andvecc= hathatj-hatk` A vector in the plane of `veca and vecb` whose projections on `vecc is 1//sqrt3` is
A. `hati+hatj-2hatk`
B. `3hati+hatj-3hatk`
C. `4hati-hatj+4hatk`
D. `4hati+hatj-4hatk`

Let `veca=hati + 2hatj +hatk, vecb=hati – hatj +hatk andvecc= hathatj-hatk` A vector in the plane of `veca and vecb` whose projections on `vecc is 1//sqrt3` is
A. `hati+hatj-2hatk`
B. `3hati+hatj-3hatk`
C. `4hati-hatj+4hatk`
D. `4hati+hatj-4hatk`
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1 Answer

  1. Correct Answer – C
    Any vector r in the plane containing a and b is `a + lambda b`
    `therefore r = ( hati + 2 hatj + hatk ) + lambda(hati-hatj+hatk)`
    `=(1+lambda)hati + (2 -lambda)hatj + (1+lambda)hatk`
    Projection of r on `c=(r*c)/(|c|)`
    `rArr ([(1+lambda)hati+(2-lambda)hatj+(1+lambda)hatk]*(hati+hatj-hatk))/(sqrt((1)^(2)+(1)^(2)+(-1)^(2)))=|(1)/(sqrt(3))|`
    `rArr (1+lambda + 2 -lambda – 1-lambda)/(sqrt(3))=|(1)/(sqrt(3))|`
    `rArr 2-lambda = pm 1 rArr lambda 1,3 `
    `therefore r = 2 hati +hatj + 2 hatk , 4 hati -hatj + 4 hatk`

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