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Position vector hat k is rotated about ...

Position vector ` hat k` is rotated about the origin by angle `135^0` in such a way that the plane made by it bisects the angel between ` hat ia n d hatjdot` Then its new position is `+-( hat i)/(sqrt(2))+-( hat j)/(sqrt(2))` b. `+-( hat i)/2+-( hat j)/2-( hat k)/(sqrt(2))` c. `( hat i)/(sqrt(2))-( hat k)/(sqrt(2))` d. none of these

A

`+-(hati)/(sqrt(2))+-(hatj)/(sqrt(2))`

B

`+-(hati)/(2)+-(hatj)/(2)-(hatk)/(sqrt(2))`

C

`(hati)/(sqrt(2))-(hatk)/(sqrt(2))`

D

none of these

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B
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Position vector hat k is rotated about the origin by angle 135^0 in such a way that the plane made by it bisects the angle between hat ia n d hatjdot Then its new position is a.+-( hat i)/(sqrt(2))+-( hat j)/(sqrt(2)) b. +-( hat i)/2+-( hat j)/2-( hat k)/(sqrt(2)) c. ( hat i)/(sqrt(2))-( hat k)/(sqrt(2)) d. none of these

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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

What is the interior acute angle of the parallelogram whose sides are represented by the vectors (1)/(sqrt(2))hat(i)+(1)/(sqrt(2))hat(j)+hat(k) and (1)/(sqrt(2))hat(i) - (1)/(sqrt(2))hat(j)+hat(k) ?

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The unit vector which is orthogonal to the vector 5hat j+2hat j+6hat k and is coplanar with vectors 2hat i+hat j+hat k and hat i-hat j+hat k is (2hat i-6hat j+hat k)/(sqrt(41)) b.(2hat i-3hat jmath)/(sqrt(13)) c.(3hat i-hat k)/(sqrt(10))d.(4hat i+3hat jmath-3hat k)/(sqrt(34))

What is the interior acute angle of the parallelogram whose sides are represented by the vectors (1)/(sqrt2) hat(i) +(2)/(sqrt2) hat(j) + hat(k) and (1)/(sqrt2) hat(i) - (1)/(sqrt2) hat(j) + hat(k) ?

A unit vector perpendicular to both hat i+ hat j\ a n d\ hat j+ hat k is hat i- hat j+ hat k b. hat i+ hat j+ hat k c. 1/(sqrt(3))( hat i+ hat j+ hat k) d. 1/(sqrt(3))( hat i- hat j+ hat k)

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