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`

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

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 \ vec a\ a n d\ vec b are two unit vectors inclined at an angle theta such that |a+b|,1, then theta (2pi)/3 c. pi/3

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

If vec a\ a n d\ vec b be two unit vectors and theta is the angle between them. Then vec a+ vec b\ is an unit vector, if theta= pi/2 b. (2pi)/3 c. pi/4 d. pi/3

L_1a n dL_2 and two lines whose vector equations are L_1: vec r=lambda((costheta+sqrt(3)) hat i+(sqrt(2)sintheta) hat j+(costheta-sqrt(3)) hat k) L_2: vec r=mu(a hat i+b hat j+c hat k) , where lambdaa n dmu are scalars and alpha is the acute angel between L_1a n dL_2dot If the angel alpha is independent of theta, then the value of alpha is a. pi/6 b. pi/4 c. pi/3 d. pi/2

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 (costheta+cos2theta)^3=cos^3theta+cos^3 2theta, then the least positive value of theta is equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2