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

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

A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(i)+hat(j)-hat(k) then the plane containing them is

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

If points A,B and C with position vectors 2 hat(i) - hat(j) + hat(k) , hat(i) - 3 hat(j) - 5hat(k) and alpha hat(i) - 3 hat(j) + hat(k) respectively are the vertices of a right-anged triangle with /_C = ( pi )/( 2) , then the values of alpha are

Find the angle between the vectors hat(i)+3hat(j)+7hat(k) and 7hat(i)-hat(j)+8hat(k) .

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

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).

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?

If vector hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3 hat(j) - a hat(k) are equal vectors, then the value of a is :