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

Find the dot product of two vectors vec(A)=3hat(i)+2hat(j)-4hat(k) and vec(B)=2hat(i)-3hat(j)-6hat(k) .

The sine of the angle between vectors vec(a)=2hat(i)-6hat(j)-3hat(k) and vec(b)=4hat(i)+3hat(j)-hat(k)

The unit vector parallel to the resultant of the vectors vec(A)= 4hat(i)+3hat(j)+6hat(k) and vec(B)= -hat(i)+3hat(j)-8hat(k) is

If vec(A) and vec(B) are perpendicular Vectors and vector vec(A)= 5hat(i)+7hat(j)-3hat(k) and vec(B)= 2hat(i)+2hat(j)-ahat(k) . The value of a is

Find th esine of angles between vectors vec(a)= 2hat(i) - 6hat(j) - 3hat(k), and vec(b) = 4hat(i) + 3hat(j)- hat(k) ?

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

Given two vectors vec(A) = -hat(i) + 2hat(j) - 3hat(k) and vec(B) = 4hat(i) - 2hat(j) + 6hat(k) . The angle made by (A+B) with x-axis is :

Find the angle between the vectors : vec(a)=2hat(i)-hat(j)+2hat(k) " and " vec(b)=6hat(i)+2hat(j)+3hat(k) .

The angle between the vectors : vec(a)=hat(i)+2hat(j)-3hat(k) and 3hat(i)-hat(j)+2hat(k) is :