If two side of a triangle are ` hat i+2 hat ja n d hat i+ hat k` , then find the length of the third side.

If the vectors bar A B=3 hat i+4 hat k and bar A C=5 hat i-2 hat j+4 hat k are the sides of a triangle ABC, then the length of the median through A is (1) sqrt(72) (2) sqrt(33) (3) sqrt(45) (4) sqrt(18)

Let hat u= hat i+ hat j , hat v= hat i- hat ja n d hat w= hat i+2 hat j+3 hat kdot If hat n is a unit vector such that hat udot hat n=0a n d hat vdot hat n=0, then find the value of | hat wdot hat n|dot

Let the position vectors of the vertices "A,B" and "C" of a triangle be 2 hat i+2 hat j+hat k,hat i+2 hat j+2 hat k and 2 hat i+hat j+2 hat k respectively.Let l_(1),l_(2)" and "l_(3) be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides "AB,BC" and "CA" respectively,then l_(1)^(2)+l_(2)^(2)+l_(3)^(2) equals:

Two sides of a triangle is represented by vec(a) = 3hat(j) and vec(b) = 2hat(i) - hat(k) . The area of triangle is :

If in parallelogram ABCD, diagonal vectors are vec A C=2 hat i+3 hat j+4 hat k and vec B D=-6 hat i+7 hat j-2 hat k , then find the adjacent side vectors vec A B and vec A D

If vec a= hat i+ hat j , vec b= hat j+ hat k , vec c= hat k+ hat i , then in the reciprocal system of vectors vec a , vec b , vec c reciprocal vec a of vector vec a is a. ( hat i+ hat j+ hat k)/2 b. ( hat i- hat j+ hat k)/2 c. (- hat i- hat j+ hat k)/2 d. ( hat i+ hat j- hat k)/2

()) The sides AB and BC of the triangle ABC are represented by the vectors 2hat i-hat j+2hat k and hat hat i+3hat hat j+5hat k respectively; find the vector representing side CA of the triangle ABC.

If the vectors vec(A) B = 3 hat(i)+4 hat (k) and vec(AC) = 5 hat(i)-2 hat(j)+4hat(k) are the sides of a triangle ABC, then the length of the median through A is

The vectors vec AB=3hat i+4hat k and vec AC=5hat i-2hat j+hat k are the sides of a triangle ABC.The length of the median through A is -