You are given vector `vec(A)=5hat(i)-6hat(j)` and `vec(B)=10hat(i)+8hat(j)`. A third vector `vec(C)` lies in the `x-y` plane. `vec(C )` is perpendicular to vector `vec(A)` and the scalar product of `vec(C )` with `vec(B)` is 100. Find the component of `vec(C )`

You are given vector vec(A)=5hat(i)-6.5hat(j) and vec(B)=10hat(i)-7hat(j) . A third vector vec(C ) lies in the x-y plane. Vector (C ) is perpendicular to vector vec(A) and the scalar product of vec(C ) with vec(B) is 15. From this information, find the component of vec(C )

If vec(A)=2hat(i)+hat(j) and vec(B)=hat(i)-hat(j) , sketch vector graphically and find the component of vec(A) along vec(B) and perpendicular to vec(B)

Given vec(A) = 3hat(i) + 2hat(j) and vec(B) = hat(i) + hat(j). The component of vector vec(A) along vector vec(B) is

If vec(a)=3hat(i)+hat(j)-4hat(k), vec(b)=6hat(i)+5hat(j)-2hat(k) and |vec(c )|=3 , find the vector vec(c ) , which is perpendicular to both vec(a) and 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 :

Let vec(a)=hat(i)+2hat(j) and vec(b)=2hat(i)+hat(j) . (i) Then, |vec(a)|=|vec(b)| (ii) Then vectors vec(a) and vec(b) are equal.

If vec(a)=2hat(i)+2 hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c)=3hat(i)+hat(j) are three vectors such that vec(a)+t vec(b) is perpendicular to vec(c) , then what is t equal to ?

If vec(a)=5hat(i)-hat(j)-3hat(k) and vec(b)=hat(i)+3hat(j)-5hat(k) , then show that the vectors (vec(a)+vec(b)) and (vec(a)-vec(b)) are perpendicular.