A non-zero vectors a is parallel to the line of intersection of the plane determined by the vectors `hat(i), hat(i)+hat(j) and ` the plane determined by the vectors `hat(i)-hat(j) and hat(i)+hat(k)`. Find the angle between a and `hat(i)-2hat(j)+2hat(k)`.

Find the angle between the vectors hat i-2 hat j+3k and 3 hat i-2 hat j+k

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

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

Unit vector along the vector hat(i) + hat(j) + hat(k) is

A vector parallel to the line of intersection of the planes overset(to)( r) (3 hat(i) - hat(j) + hat(k) )=5 and overset(to) (r ) (hat(i) +4 hat(j) - 2 hat(k) )=3 is

If the vectors hat(i)+hat(j)+hat(k) makes angle alpha, beta and gamma with vectors hat(i), hat(j) and hat(k) respectively, then

Find the area of the parallelogram determined by the vectors: 2 hat i+ hat j+3 hat k\ a n d\ hat i- hat j

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

Let A be vector parallel to line of intersection of planes P_1 and P_2 . Plane P_1 is parallel to the vectors 2hat(j)+3hat(k) and 4hat(j)-3hat(k) and that P_2 is parallel to hat(j)-hat(k) and 3hat(i)+3hat(j) , then the angle between vector A and a given vector 2hat(i)+hat(j)-2hat(k) is

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot