एक प्रक्षेप्य को ` (hat(i) + 2 Hat (j) ) m//s` का प्रारंभिक वेग दिया गया है, जहां `hat(i)` है...

A projectile is given an initial velocity of ( hat(i) + 2 hat (j) ) m//s , where hat(i) is along the ground and hat (j) is along the vertical . If g = 10 m//s^(2) , the equation of its trajectory 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

Show that the following points whose position vectors are given are collinear : (i) 5 hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and - 4 hat(i) + 3 hat(j) - hat(k) (ii) - 2 hat(i) + 3 hat(j) + 5 hat(k), hat(i) + 2 hat(j) + 3 hat(k) and 7 hat(i) - hat(k) .

If vec(F ) = (60 hat(i) + 15 hat(j) - 3 hat(k)) N and vec(V) = (2 hat(i) - 4 hat(j) + 5 hat(k)) m/s, then instantaneous power is:

Find the projection of vec(a) = 2 hat(i) - hat(j) + hat(k) on vec(b) = hat(i) - 2 hat(j) + hat(k) .

The unit vector perpendicular to the plane passing through point P( hat i- hat j+2 hat k),\ Q(2 hat i- hat k)a n d\ R(2 hat j+ hat k)i s a) dot""2 hat i+ hat j+ hat k"\" b. sqrt(6)(2 hat i+ hat j+ hat k) c. 1/(sqrt(6))(2 hat i+ hat j+ hat k) d. 1/6(2 hat i+ hat j+ hat k)

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

If vec(a)=hat(i)-hat(j)+hat(k), vec(b) = 2 hat(i) + 3 hat( j) + 2 hat(k) and vec(c) = hat(i) - m hat(j) + n hat(k) are three coplanar vectors and |vec(c)|=sqrt(6) , then which one of the following is correct?

If vec a= hat i+ hat j , vec b= hat j+ hat k , vec c= hat k+ hat i , then in the reciprocal system of vectors vec a , vec b , vec c reciprocal vec a of vector vec a is a. ( hat i+ hat j+ hat k)/2 b. ( hat i- hat j+ hat k)/2 c. (- hat i- hat j+ hat k)/2 d. ( hat i+ hat j- hat k)/2