Let `bara=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 `barb-bar a and bar d-bar c` are parallel and find the ratio of their moduli.

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

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

bar A = 2 hat i + 3 hat j and bar b = 3 hat i + 5 hat j Then bar a xx 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

Let bar a= hat i+ hat j+ hat k ,""b= hat i- hat j+2 hat k and bar c=x hat i+(x-2) hat j- hat k . If the vector c lies in the plane of a and b , then x equals

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 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]|

The angle between the vectors bar(A) and bar B , where bar(A)=hat i+2hat j-hat k and bar(B)=-hat i+hat j-2hatk is