If for two vectors `hat(A)` and `hat(B)`,sum `(vec(A)+vec(B))` is perpendicular to the diffrence `(vec(A)-vec(B))`. Find the ratio of their magnitude.

There are two vector vec(A)=3hat(i)+hat(j) and vec(B)=hat(j)+2hat(k) . For these two vectors- (i) Find the component of vec(A) along vec(B) and perpendicular to vec(B) in vector form. (ii) If vec(A) & vec(B) are the adjacent sides of parallelogram then find the magnitude of its area. (iii) Find a unit vector which is perpendicular to both vec(A) & vec(B) .

There are two vector vec(A)=3hat(i)+hat(j) and vec(B)=hat(j)+2hat(k) . For these two vectors- (i) Find the component of vec(A) along vec(B) and perpendicular to vec(B) in vector form. (ii) If vec(A) & vec(B) are the adjacent sides of parallelogram then find the magnitude of its area. (iii) Find a unit vector which is perpendicular to both vec(A) & vec(B) .

Two vectors vec(A) and vec(B) lie in X-Y plane. The vector vec(B) is perpendicular to vector vec(A) . If vec(A) = hat(i) + hat(j) , then vec(B) may be :

Two vectors vec(A) and vec(B) lie in X-Y plane. The vector vec(B) is perpendicular to vector vec(A) . If vec(A) = hat(i) + hat(j) , then vec(B) may be :

If there are two vectors vec(A) and vec(B) such that vec(A)+vec(B)=hat(i)+2hat(j)+hat(k) and vec(A)-vec(B)=(hat(i)-vec(k)) , then choose the correct options.

If there are two vectors vec(A) and vec(B) such that vec(A)+vec(B)=hat(i)+2hat(j)+hat(k) and vec(A)-vec(B)=(hat(i)-vec(k)) , then choose the correct options.

If vec(a)=2hat(i)+5hat(j)-2hat(k) " and " vec(b)=hat(i)-hat(j)+hat(k) , then find (i) vec(a)+vec(b) " and " 2vec(a)-3vec(b) " " (ii)abs(vec(a)+vec(b)) " and " abs(vec(a)-2vec(b)) (iii) a unit vector in the direction (vec(a)+vec(b)) (iv) vector and scalar components of the vector (2vec(a)-3vec(b)) along the coordinate axes.

For any two vectors vec a and hat b, show that (vec a+vec b)*(vec a-vec b)=0hat harr|vec a|=|vec b|

Given vec a = 4 hat i - hat j + 3 hat k and vec b = -2 hat i + hat j - 2 hat k . (i) Find a unit vector perpendicular to both vec a and vec b . (ii) Find a vector of magnitude 9 which is perpendicular to both vec a and vec b .