Let a, b and c are three vectors hacing magnitude 1, 2 and 3 respectively satisfying the relation [a b c]=6. If `hat(d)` is a unit vector coplanar with b and c such that `b*hat(d)=1`, then evaluate `|(axxc)*d|^(2)+|(axxc)xxhat(d)|^(2)`.

If a, b and c are three vectors qith magnitudes 1, 1 and 2 respectively and axx(axxc)+b=0_(') then the angle between a and c is

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

Given four non zero vectors bar a,bar b,bar c and bar d. The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

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