[" 22.Two particles having position vectors "bar(r)_(1)=(3bar(j)+5 boldsymbol j)m" arid "r=(-5i+3 boldsymbol j)m" are moving with velocities "],[qquad bar(J)_(1)=(4hat i-4j)ms^(-1)" and "Gamma_(2)=(aj-3)ms^(-1)" if they collide after "2" seconds,the value of a is "]

Two particles having position vectors vec(r )_(1) = ( 3 hat(i) + 5 hat(j)) meters and vec( r)_(2) = (- 5 hat(i) - 3 hat(j)) metres are moving with velocities vec(v)_(1) = ( 4 hat(i) + 3 hat(j)) m//s and vec(v)_(2) = (alpha hat(i) + 7 hat(j)) m//s . If they collide after 2 s , the value of alpha is

The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)+4bar(j)+2bar(k) and 4bar(i)+2bar(j)+3bar(k) are the vertices of

Show that the four points with position vectors 3bar(i)+5bar(j), 3bar(j)-5k, 5bar(i)-19bar(j)-3bar(k), 6bar(i)-5bar(j) are non coplanar.

A particle velocity changes from (2hat(i)+3hat(j))ms^(-1) to (2hat(i)-3hat(j))ms^(-1) in 2 s. The acceleration in ms^(-2) is

A particle velocity changes from (2hat(i)+3hat(j))ms^(-1) to (2hat(i)-3hat(j))ms^(-1) in 2 s. The acceleration in ms^(-2) is

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

The vectors bar(i)+4bar(j)+6bar(k),2bar(i)+4bar(j)+3bar(k) and bar(i)+2bar(j)+3bar(k) form