Let `hat a , hat b , hatc ` be unit vectors such that ` hat a * hatb =hat a *hatc =0 ` and the angle between` hat b and hat c ` be ` (pi)/(6) ` prove that ` hat a =+- 2 (hatb xx hat c ) `

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 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 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

Let hat a , hat b ,and hat c be the non-coplanar unit vectors. The angle between hat b and hat c is alpha , between hat c and hat a is beta and between hat a and hat b is gamma . If A( hat a cosalpha, 0),B( hat bcosbeta, 0) and C( hat c cosgamma, 0), then show that in triangle AB C , (|hat axx(hat bxx hat c)|)/(sinA)=(|hat bxx(hat cxx hat a)|)/(sinB)=(|hat cxx(hat axx hat b)|)/(sinC)

If hat i ,\ hat j ,\ hat k\ are unit vectors, then hat idot hat j=1 b. hat idot hat i=1 c. hat ixx hat j=1 d. hat ixx( hat jxx hat k)=1

Let a= 2hat(i) -2hat(k) , b=hat(i) +hat(j) and c be a vectors such that |c-a| =3, |(axxb)xx c|=3 and the angle between c and axx b" is "30^(@) . Then a. c is equal to

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

Find the angle between two vectors A= 2 hat i + hat j - hat k and B=hat i - hat k .

Given unit vectors hat m , hat na n d hat p such that angel between hat ma n d hat n is alpha and angle between hat pa n d( hat mxx hat n) is also alpha,then[ hat n hat p hat m]=

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|)