Let `bar(AB)=3 hat i-hat j,bar(AC)=2 hat i+3 hat j` and `bar(DE)=4 hat i-2 hat j`. The area of the shaded region in the adjacent figure, is

Let bar(AB)=3hat i-hat j,bar(AC)=2hat i+3hat j and bar(DE)=4hat i-2hat j .The area of the shaded region in the adjacent figure,is

In given figure vec A B=3 hat i- hat j , vec A C=2 hat i+3 hat j and DE= 4 hat i-2 hat j . Then the area of the shaded region is (a)5 (b) 6 (c) 7 (d)(8)

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

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= 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)=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.

Let bar(a)= hat(i) + hat(j) + hat(k), bar(b)= hat(i) + 3hat(j) + 5hat(k) and bar(c )= 7hat(i) + 9hat(j) + 11hat(k) . Then, the area of the parallelogram with diagonals bar(a) + bar(b) and bar(b) + bar(c ) is