If `hat(a),hat(b),hat(c)` are three unit vectors such that `hat(b)andhat(c)` are non-parallel and `hat(a)xx(hat(b)xxhat(c))=(1)/(2)hat(b)," find the angle between "vec(a)andvec(c).`

Let hat(a) , hat(b) " and " hat( c) be three unit vectors such that hat(a) xx (hat(b) xx hat( c)) = (sqrt(3))/(2)( hat(b) +hat(c )). If hat(b) is not parallel to hat( c) then the angle between hat(a) " and " hat(b) is

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

Two vectors vec(A) = hat(i) + 2 hat(j) + 2 hat(k) and vec(B) = hat(i) + 3 hat(j) + 6 hat(k) find . angle between them .

Consider the vectors vec a = hat i - 7 hat j + 7 hat k, 3 hat i - 2 hat j + 2 hat k (a) Find vec a.vecb (b) Find the angle between vec a and vec b .

Consider the vectors veca = hat i + 3 hat j + hat k and vec b = 2 hat i - hat j - hat k . (i) Find vec a.vec b (ii) Find the angle between vec a and vec b .

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

The edges of a parallelopied are of unit length and are parallel to non- coplanar unit vector hat(a), hat(b) , hat(c ) such that hat(a) , hat(b) = hat(b), hat( c)=hat(c ), hat(a) = .(1)/(2). Then the volume of the parallelopiped is

vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=-hat(i)+2hat(j)-4hat(k),vec(c)=hat(i)+hat(j)+hat(k)" then find the of "(vec(a)xxvec(b))*(vec(a)xxvec(c)).

Let overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(b) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(c) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k) be three non- zero vectors such that overset(to)(c ) is a unit vectors perpendicular to both the vectors overset(to)(c ) and overset(to)(b) . If the angle between overset(to)(a) " and " overset(to)(n) is (pi)/(6) then |{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}|^2 is equal to