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

Find the angle between the vectors : vec(a)=3vec(i)-2vec(j)+vec(k) and vec(b)=vec(i)-2vec(j)-3vec(k)

Find the unit vectors perpendicular to both the vectors 2vec(i)- 3vec(j) + 5vec(k) and -vec(i) + 4vec(j) + 2vec(k)

Any vector which is perpendicular to each of the vectors 2vec(i) + vec(j) -vec(k) and 3vec(i) -vec(j) + vec(k) is normal to

Find the angle between the planes vec(r).(2vec(i)-vec(j)+2vec(k))=3 an vec(r).(3vec(i)+6vec(j)+vec(k))=4 .

Find a vector of magnitude and perpendicular to both the vectors vec(a)= 2vec(i)- 2vec(j) + vec(k) and vec(b)= 2vec(i) + 2vec(j) + 3vec(k)

The sine of the angle between the vectors vec i+3vec j+2vec k and 2vec i-4vec j+vec k is

The vector area of the parallelogram whose adjacent sides vec(i) + vec(j) + vec(k) and 2vec(i)-vec(j) + 2vec(k) is

Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

Find the angle between the line vec r=( vec i+2 vec j- vec k)+lambda( vec i- vec j+ vec k) and the normal to the plane vec rdot((2 vec i- vec j+ vec k))=4.