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Vector ` vec a` in the plane of ` vec b=2 hat i+ hat ja n d vec c= hat i- hat j+ hat k` is such that it is equally inclined to ` vec ba n d vec d` where ` vec d= hat j+2 hat kdot` The value of` vec a` is a.`( hat i+ hat j+ hat k)/(sqrt(2))` b. `( hat i- hat j+ hat k)/(sqrt(3))` c. `(2 hat i+ hat j)/(sqrt(5))` d. `(2 hat i+ hat j)/(sqrt(5))`

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If a unit vector hat a in the plane of vec b=2 hato+ hat j& vec c= hat i- hat j+ hat k is such that vec a vec d where vec d= hat j+2 hat l , then hat a is ( hat i+ hat j+ hat k)/(sqrt(3)) (b) ( hat i- hat j+ hat k)/(sqrt(3)) (2 hat i+ hat j)/(sqrt(5)) (d) (2 hat i- hat j)/(sqrt(5))

Let vec a= hat i- hat j , vec b= hat j- hat ka n d vec c= hat k- hat i. If vec d is a unit vector such that vec a.vec d=0=[ vec b vec c vec d], then d equals a. +-( hat i+ hat j-2 hat k)/(sqrt(6)) b. +-( hat i+ hat j- hat k)/(sqrt(3)) c. +-( hat i+ hat j+ hat k)/(sqrt(3)) d. +- hat k

If vec a = hat i + hat j, vec b = hat i + hat k, vec c = hat k + hat i, a unit vector parallel to vec a + vec b + vec c

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

If vec a= hat i+ hat j , vec b= hat j+ hat k , vec c= hat k+ hat i , then in the reciprocal system of vectors vec a , vec b , vec c reciprocal vec a of vector vec a is a. ( hat i+ hat j+ hat k)/2 b. ( hat i- hat j+ hat k)/2 c. (- hat i- hat j+ hat k)/2 d. ( hat i+ hat j- hat k)/2

If vec A = hat i + 3 hat j + 2 hat K and vec B = 3 hat i + hat j + 2 hat k , then find the vector product vec A xx vec B .

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The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

vec a=2hat i-hat j+hat k,vec b=hat i+hat j-2hat k and vec c=hat i+3hat j-hat k,f in d lambda such that vec a is perpendicular to lambdavec b+vec c

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