If `bar(r)` is a vector satisfying `bar(r)times(hat i+hat j+2hat k)=hat i-hat j`, then `|bar(r)|` can be

If t is a real number, and a vector vec r satisfies the equation vec r times(hat i-2hat j+hat k)=hat i-hat k , then vec r can be equal to- (A) hat j+t(hat i-2hat j+hat k) (B) hat i-hat j+hat k (C) 2hat i-3hat j+2hat k (D) hat i+hat k

If bar(P)=hat i+hat j+hat k,bar(Q)=2hat i-hat j-hat k , then bar(P)-bar(Q) is

If bar(a)=3hat i-3hat j-4hat k, bar(b)=hat i+2hat j+hat k and bar(c)=3hat i-hat j-2hat k , then [bar(a) bar(b) bar(c)] =

If bar(a) and bar(b) are vectors such that |bar(a)+bar(b)|=sqrt(29) and bar(a)times(2hat i+3hat j+4hat k)=(2hat i+3hat j+4hat k)timesbar(b) then the value of (bar(a)+bar(b)).(-7hat i+2hat j+3hat k) is .......

If bar(a) is any vector the value of hat i times(bar(a)times hat i)+hat j times(bar(a)times hat j)+hat k times(bar(a)times hat k)=

Let bar(a)=4hat i+3hat j-hat k,bar(b)=5hat i+2hat j+2hat k,bar(c)=2hat i-2hat j)-3hat k and bar(d)=4hat i-4hat j+3hat k; prove that bar(b)-bar(a) and bar(d)-bar(c) are parallel and find the ratio of their moduli.

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

If bar a=hat i +hat j+ hat k, bar b=hat i-hat j +hat k, bar c=hat i +2hat j-hat k then the value of |[bar a.bar a, bar a.bar b, bar a.bar c],[bar b.bar a,bar b.bar b, bar b.bar c],[bar c.bar a,bar c.bar b,bar c.barc]|

A line passes through (3, -1, 2) and perpendicualr to thelines bar r = (hat i +hat j - hat k)+ lambda(2 hat i -2 hat j +hat k )" and " bar r= (2 hat i + hat j -3 hatk )+ mu( hat i-2 hat j +2 hat k), find its equation .

If the vectors bar(a)=3hat i+hat j-2hat k,bar(b)=-hat i+3hat j+4hat k&bar(c)=4hat i-2hat j-6hat k constitute the sides of a Delta ABC, then the length of the median bisecting the vector bar(c) is