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)] =

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.

If bar a=hat i+hat j-4hat k and bar(b)=hat 4i-hat j-2hat k then find (i) a unit vector in the direction of the vector (2bar(a)-bar(b))

If bar(a)=hat i+hat j+2hat k, bar(b)=hat i+2hat j+2hat k and |bar(c)_(1)|=1 ,then the maximum value of [bar(a)timesbar(b) quad bar(b)timesbar(c) quad bar(c)timesbar(a)] is

Let bar(a)=hat j-hat k and bar(c)=hat i-hat j-hat k then the vector bar(b) satisfying bar(a)timesbar(b)+bar(c)=0 and bar(a).bar(b)=3 is

If bar(a)=2hat i+2hat j+hat k and bar(b)=hat i-hat j-chat k .If angle between bar(a) and bar(b) is 37^(0) .The value of c is (take, cos37^(0)=(4)/(5)

If bar(A)=2hat i+3hat j+6hat k and bar(B)=3hat i-6hat j+2hat k ,then a vector perpendicular to both bar(A) and bar(B) has magnitude K times that of (6hat i+2hat j-3hat k) .Then K is equal to

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]|

Let bar(a)=3hat i+2hat j+2hat k,bar(b)=hat i+2hat j-2hat k Then a unit vector perpendicular to both bar(a)-bar(b) and bar(a)+bar(b) is

Let bar(a)=3hat i+2hat j+2hat k , bar(b)=hat i+2hat j-2hat k .Then a unit vector perpendicular to both bar(a)-bar(b) and bar(a)+bar(b) is