Two adjacent sides of a parallelogram `A B C D` are `2 hat i+4 hat j-5 hat k` and ` hat i+2 hat j+3 hat k` . Then the value of `|A CxxB D|` is `20sqrt(5)` b. `22sqrt(5)` c. `24sqrt(5)` d. `26sqrt(5)`

Show that the area of a parallelogram having diagonals 3hat i+hat j-2hat k and hat i-3hat j+4hat k is 5sqrt(3) square units.

Two adjacent sides of a parallelogram A B C D are given by vec A B=2 hat i+10 hat j+11 hat ka n d vec A D=- hat i+2 hat j+2 hat kdot The side A D is rotated by an acute angle alpha in the plane of the parallelogram so that A D becomes A D^(prime)dot If A D ' makes a right angle with the side A B , then the cosine of the angel alpha is given by 8/9 b. (sqrt(17))/9 c. 1/9 d. (4sqrt(5))/9

If theta is the angle between the vectors 2 hat i-2 hat j+4 hat k\ a n d\ 3 hat i+ hat j+2 hat k , then sintheta= 2/3 b. 2/(sqrt(7)) c. (sqrt(2))/7 d. sqrt(2/7)

The angle between the two vectors vec A= 3 hat i + 4 hat j + 5 hat k and vec B = 3 hat i + 4 hat j + 5 hat k will be

The diagonals if a parallele-gram are representde by vec d_(1) =2 hat I + 3 hat j -5 hat k and vec d_(2) =6 hat I + 5 hat j -3 hat k . Find the area of the parallelogram.

If vec A=2hat i+3hat j-hat k and vec B=-hat i+3hat j+4hat k ,then projection of A on B will be (n)/(sqrt(26)) then n is

If vec a=hat i-2hat j+hat k,vec b=2hat i+hat j-hat k and vec C=3hat i+5hat j+2hat k then find the value of vec a xx(vec b xxvec c)

If ABCD is a parallelogram, vec A B=2 hat i+4 hat j-5 hat k and vec A D= hat i+2 hat j+3 hat k , then the unit vector in the direction of B D is 1/(sqrt(69))( hat i+2 hat j-8 hat k) (b) 1/(69)( hat i+2 hat j-8 hat k) 1/(sqrt(69))(- hat i-2 hat j+8 hat k) (d) 1/(69)(- hat i-2 hat j+8 hat k)

The sides of a parallelogram are 2hat i+4hat j-5hat k and hat i+2hat j+3hat k .The unit vector parallel to one of the diagonals is a.(1)/(7)(3hat i+6hat j-2hat k) b.(1)/(7)(3hat i-6hat j-2hat k) c.(1)/(sqrt(69))(hat i+6hat j+8hat k) d.(1)/(sqrt(69))(-hat i-2hat j+8hat k)

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.