The vectors `vec(a)=(2-x)hat(i)+2 hat(j)+2hat(k)," "vec(b) = 2hat(i)+(2-y)hat(j)+2hat(k)," "vec(c)=2hat(i)+2hat(j)+(2-z)hat(k) and vec(d) = hat(i) +hat(j)+hat(k)` are coplanar, then

The angle between vec(A) = hat(i) = 2hat(j) - hat(k) and vec(B) = - hat(i) + hat(j) - 2hat(k) is

If vec(a)=2hat(i)+3hat(j)+hat(k), vec(b)=hat(i)-2hat(j)+hat(k) and vec(c )=-3hat(i)+hat(j)+2hat(k) , find [vec(a)vec(b)vec(c )] .

Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

Write the projection of vec(b) + vec(c ) on vec(a) , where vec(a) = 2hat(i) - 2hat(j) + hat(k), vec(b) = hat(i) + 2hat(j) - 2hat(k) and vec(c ) = 2hat(i) - hat(j) + 4hat(k) .