Show that the vectors `hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k)` are coplanar.

What is the value of m if the vectors 2hat(i)-hat(j)+hat(k), hat(i)+2hat(j)-3hat(k) and 3hat(i)+m hat(j)+5 hat(k) are coplanar?

Show that the vectors 2hat(i)-hat(j)+hat(k) and hat(i)-3hat(j)-5hat(k) are at right angles.

If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+hat(j)+chat(k) , where a, b, c are coplanar, then a+b+c-abc=

Find the value of lamda , if the points with position vectors 3hat(i)- 2hat(j)- hat(k), 2hat(i) + 3hat(j)- 4hat(k), -hat(i) + hat(j) + 2hat(k), 4hat(i) + 5hat(j) + lamda hat(k) are coplanar.

The vectors 3 hat(i)- hat(j) + 2 hat(k) , 2 hat(i) + hat(j) + 3 hat(k) and hat(i) + lambdahat(j) - hat(k) are coplanar if the value of lambda is (i) -2 (ii) 0 (iii) 2 (iv) any real number

The value of 'a' so that the vectors 2 hat(i) - 3hat(j) + 4hat(k) and a hat(i) + 6hat(j) - 8hat(k) are collinear

Show that the vectors vec(A) = 2 hat(i) - 3 hat(j)-1hat(k) and vec(B) = - 6hat(i) +9 hat(j) +3 hat(k) are parallel .

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k form the vertices of a right angled triangle.

Find the angle between the vectors 2 hat(i) - hat(j) - hat(k) and 3 hat(i) + 4 hat(j) - hat(k) .