`|[i,j,k],[2,3,6],[3,-6,2]|=?`

If a=(1)/(7)(2hat(i)+3hat(j)+6hat(k)): b=(1)/(7)(6hat(i)+2hat(j)-3hat(k)): c=c_1hat(i)+c_2hat(j)+c_2hat(k) and matrix A=[[(2)/(7), (3)/(7), (6)/(7)], [(6)/(7), (2)/(7), -(3)/(7)], [c_1, c_2, c_3]] and AT^(T)=I , then c

show that given vectors are coplaner i-2j+3k,-2i+3j-4k,-j+2k

Let the centre of the parallelepiped formed by vec P A= hat i+2 hat j+2 hat k ; vec P B=4 hat i-3 hat j+ hat k ; vec P C=3 hat i+5 hat j- hat k is given by the position vector (7, 6, 2). Then the position vector of the point P is (3,4,1) (b) (6,8,2) (1, 3, 4) (d) (2, 6, 8)

The P.V.'s of the vertices of a triangle are 2i+3j+4k,4i+6k+3k,3i+2j+3k P.V.of orthocentre is :

The vector [(i-j+k) times (2i-3j-k)] times [(-3i+j+k) times (2j+k)] is given by