If the vectors `a=hat(i)-hat(j)+2hat(k), b=2hat(i)+4hat(j)+hat(k) and c=lambdahat(i)+hat(j)+muhat(k)` are mutually orthogonal, then `(lambda, mu)` is equal to

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

If a=hat(i)+2hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=hat(i)+3hat(j)-hat(k) , then atimes(btimesc) is equal to

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

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=

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

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

Examine whether the vectors a=2hat(i)+3hat(j)+2hat(k), b=hat(i)-hat(j)+2hat(k) and c=4hat(i)+2hat(j)+4hat(k) form a left handed or a right handed system.

Find the unit vector perpendicular to both 2hat(i) + 3hat(j)+ hat(k) and hat(i)-hat(j)+ 4hat(k)

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 :

Three vectors vec(A) = 2hat(i) - hat(j) + hat(k), vec(B) = hat(i) - 3hat(j) - 5hat(k) , and vec(C ) = 3hat(i) - 4hat(j) - 4hat(k) are sides of an :