InterviewSolution
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InterviewSolution
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Let ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k`be three vectors. A vector ` vec v`in the plane of ` vec aa n d vec b ,`whose projection on ` vec c`is `1/(sqrt(3))`is given by` hat i-3 hat j+3 hat k`b. `-3 hat i-3 hat j+3 hat k`c. `3 hat i- hat j+3 hat k`d. ` hat i+3 hat j-3 hat k`A. `3 hat(i)+hat(j)-3hat(k)`B. `3hat(i)-hat(j)+3hat(k)`C. `3hat(i)+hat(j)+3hat(k)`D. `-3hat(i)+hat(j)+3hat(k)` |
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Answer» Correct Answer - B Here, `(v.c)/(|c|) = 1/(sqrt(3))` `rArr (v.c)/(sqrt(1+1+1)) = 1/(sqrt(3))` `rArr (v.c)/(sqrt(3)) = 1/(sqrt(3)) rArr v.c = 1` `rArr v.(hati-hatj -hatk) = 1 "….."(i)` we get from option (b) `v=3 hati-hatj+3hatk` ` v.c (3hati -hatj+3hatk)` `=3+1-3=1` which satisfies Eq. 9i) `v=3hati-hatj+3hatk` |
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