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\ 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 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 a and hatb are two unit vectors inclined at an angle theta , then sin(theta/2)

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 , hat b ,a n d hat c are three unit vectors inclined to each other at angle theta, then the maximum value of theta is pi/3 b. pi/4 c. (2pi)/3 d. (5pi)/6

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

If hat a ,\ hat b are unit vector such that \ hat a+ hat b is a unit vectors, write the value of | hat a- hat b|dot

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

If hat a , hat b ,a n d hat c are unit vectors, then | hat a+hat b|^2+| hat b- hat c|^2+| hat c- hat a|^2 does not exceed

If hat a , hat b ,a n d hat c are three unit vectors, such that hat a+ hat b+ hat c is also a unit vector and theta_1,theta_2a n dtheta_3 are angles between the vectors hat a , hat b ; hat b , hat ca n d hat c , hat a respectively, then among theta_1,theta_2,a n dtheta_3dot a. all are acute angles b. all are right angles c. at least one is obtuse angle d. none of these