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

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)=3hat(i)-2hat(j)+7hat(k),bar(b)=5hat(i)+hat(j)-2hat(k)andbar(c)=hat(i)+hat(j)-hat(k) , then find bar(a)*(bar(b)xxbar(c)) .

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]|

If bar(a)=3hat(i)-hat(j)+4hat(k)," "bar(b)=2hat(i)+3hat(j)-hat(k)," "bar(c)=-5hat(i)+2hat(j)+3hat(k) , then bar(a)*(bar(b)xxbar(c)) = . . . . . . . .

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

If bar(a)=phat i+3hat j-7hat k, bar(b)=phat i-phat j+4hat k and if the angle between bar(a) and bar(b) is acute, then the values of p lies in.

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

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

If vec a=3hat i-hat j-4hat k,vec b=2hat i+4hat j-3hat k and vec c=hat i+2hat j-widehat k, find |3vec a-2hat b+4hat c|