If `hat(a) and hat(b)` are unit vectors and `theta` is the angle between them, prove that `"tan"(theta)/(2)= (|hat(a)-hat(b)|)/(|hat(a)+ hat(b)|)`

If hat a\ a n d\ hat b are unit vectors inclined at an angle theta then prove that tantheta/2=(| hat a- hat b|)/(| hat a+ hat b|)

If hat aa n d hat b are unit vectors inclined at an angle theta , then prove that sintheta/2=1/2| hat a- hat b|dot

If hat a and hat b are unit vectors inclined at an angle theta , then prove that costheta/2=1/2| hat a+ hat b| tantheta/2=1/2|( hat a- hat b)/( hat a+ hat b)|

If hat u and hat v are unit vectors and theta is the acute angle between them, then 2 hat uxx3 hat v is a unit vector for (1) exactly two values of theta (2) more than two values of theta (3) no value of theta (4) exactly one value of theta

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

Let hat(u), hat(v) and hat(w) are three unit vectors, the angle between hat(u) and hat(v) is twice that of the angle between hat(u) and hat(w) and hat(v) and hat(w) , then [hat(u) hat(v) hat(w)] is equal to

If hat(a), hat(b) and hat(c) are the three unit vector and alpha, beta and gamma are scalars such that hat(c)=alphahat(a)+betahat(b)+gamma(hat(a)xxhat(b)). If is given that hat(a)*hat(b)=o and hatc makes equal angle with both hat(a)and hat(b) , then evaluate alpha^(2)+beta^(2)+gamma^(2) .

If hat(i), hat(j) and hat(k) represent unit vectors along the x, y and z axes respectively, then the angle theta between the vectors (hat(i) + hat(j) + hat(k)) and (hat(i) + hat(j)) is equal to :

The angle between A=hat(i)+hat(j) " and " B=hat(i)-hat(j) is

Unit vector hat(P) and hat(Q) are inclined at an angle theta . Prove that |hat(P)-hat(Q)|= 2 sin(theta//2) .