If `|vec(V)_(1)+vec(V)_(2)|=|vec(V)_(1)-vec(V)_(2)|and V_(2)` is finite, then

If vec(v)_(1)+vec(v)_(2) is perpendicular to vec(v)_(1)-vec(v)_(2) , then

If vec(v)_(1)+vec(v)_(2) is perpendicular to vec(v)_(1)-vec(v)_(2) , then

Let vec(V_(1))=hati+ahatj+hatk, vec(V_(2))=hatj+ahatk and vec(V_(3))=ahati+hatk, AA a gt 0. If [(vec(V_(1)),vec(V_(2)),vec(V_(3)))] is minimum, then the value of a is

Let vec(V_(1))=hati+ahatj+hatk, vec(V_(2))=hatj+ahatk and vec(V_(3))=ahati+hatk, AA a gt 0. If [(vec(V_(1)),vec(V_(2)),vec(V_(3)))] is minimum, then the value of a is

Let vec(v_1) , vec(v_2) , vec(v_3), vec(v_4) be unit vectors in the xy-plane, one each in the interior of the four quadrants. Which of the following statements is necessarily ture. ?

If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and |vec(a)| =|vec(b)|=2, (vec(a), vec(b)) =(pi)/(3) , then |vec(u) xx vec(v)| =

Two particles of masses m_(1) and m_(2) in projectile motion have velocities vec(v)_(1) and vec(v)_(2) , respectively , at time t = 0 . They collide at time t_(0) . Their velocities become vec(v')_(1) and vec(v')_(2) at time 2 t_(0) while still moving in air. The value of |(m_(1) vec(v')_(1) + m_(2) vec(v')_(2)) - (m_(1) vec(v)_(1) + m_(2) vec(v)_(2))|