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

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

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

If unit vectors hat(a) and hat(b) are inclined at angle theta , then prove that |vec(a) - vec(b)| = 2 sin.(theta)/(2) .

Let two non-collinear unit vector hat a a n d hat b form an acute angle. A point P moves so that at any time t , the position vector O P(w h e r eO is the origin) is given by hat acost+ hat bsintdotW h e nP is farthest from origin O , let M be the length of O Pa n d hat u be the unit vector along O Pdot Then (a) hat u=( hat a+ hat b)/(| hat a+ hat b|)a n dM=(1+ hat adot hat b)^(1//2) (b) hat u=( hat a- hat b)/(| hat a- hat b|)a n dM=(1+ hat adot hat )^(1//2) (c) hat u=( hat a+ hat b)/(| hat a+ hat b|)a n dM=(1+2 hat adot hat b)^(1//2) (d) hat u=( hat a- hat b)/(| hat a- hat b|)a n dM=(1+2 hat adot hat b)^(1//2)

Let hat(a), hat(b) be two unit vectors and theta be the angle between them. What is cos ((theta)/(2)) equal to ?

Let hat(a), hat(b) be two unit vectors and 0 be the angle between them. What is cos ((theta)/(2)) equal to ?

If hat a and hat b are unit vectors such that [ hata hatb hatatimeshatb ]= (1)/(4) ,then the angle between hat a and hat b ,is equal to

Let hat(a), hat(b) be two unit vectors and 0 be the angle between them. What is sin ((theta)/(2)) equal to