10 কেজি ভরের একটি শরীরে যে বল কাজ করে তা হল (2 ওভারসেট ^i +j -ওভারসেট ^k ) N. যদি শরীরটি ini হয়...

The force acting on a body of mass 10 kg is (2 overset ^i +j -overset ^k ) N. If the body is initially at rest, then velocity at the end of 20 sec will be

Let s_1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} , s_2 = {(i,j) ∶ 1 ≤ i s_3 = {(i,j, k, l) ∶ 1 ≤ i s_4 = {(i,j, k, l) ∶ i,j, k and l are distinct elements in {1,2, … ,10}} . If the total number of elements in the set s_r is n_r , r= 1,2,3,4, then which of the following statements is (are) TRUE ?

A particle moves with the velocity vec v = (5 vec i + 2 vec j - vec k) ms^(-1) under the influence of a constant force, vec F = (2 vec i + 5 vec j - 10 vec k)N . The instantaneous power applied is

A motor boat is going in a river with a velocity vec(V) = (4 hat i-2 hat j + hat k) ms^(-1) . If the resisting force due to stream is vec (F)=(5 hat i-10 hat j+6 hat k)N , then the power of the motor boat is

When a proton has a velocity vec v = (2hat i + 3 hat j) xx 10^6 ms^-1 , it experiences a force vec F = -(1.28 xx 10^(-13) hat k) N. When its velocity is along the z-axis, it experiences a force along the x-axis. What is the magnetic field?

The ratio in which the plane vec rdot( vec i-2 vec j+3 vec k)=17 divides the line joining the points -2 vec i+4 vec j+7 vec ka n d3 vec i-5 vec j+8 vec k is a. 1:5 b. 1: 10 c. 3:5 d. 3: 10

Find the vector and Cartesian forms of the equation of the plane passing through the point (1,\ 2,\ -4) and parallel to the lines vec r=( hat i+2 hat j-4 hat k)+lambda(2 hat i+3 hat j+6 hat k)a n d\ vec r=( hat i-3 hat j+5 hat k)+mu( hat i+ hat j- hat k)dot Also find the distance of the point (9, -8, -10) from the plane thus obtained.

If vec a=2 hat i-3 hat j- hat k\ a n d\ b= hat i+4 hat j-2 hat k ,\ t h e n\ vec axx vec b= a. 10 hat i+2 hat j+11 hat k b. 10 hat i+3 hat j+11 hat k c. 10 hat i-3 hat j+11 hat k d. 10 hat i-2 hat j-10 hat k

Give the order of the following : (a) 1 (b) 1000 (c ) 499 (d) 500 (e) 501) (f) 1 AU (1.496 xx 10^(11) m) (g) 1 Å (10(-10)m ) (h) Speed of light (3.00 xx 10^(8) m//s) (i) Gravitational constant (6.67 xx 10^(-11) N-m^(2)//kg^(2)) (j) Avogadro constant (6.02 xx 10^(23) mol^(-1)) (k) Planck's constant (6.63 xx 10^(-34) J-s) (l) Charge on electron (1.60 xx 10^(-19) C) (m) Radius of H - atom (5.29 xx 10^(-11)m) (n) Atmospheric pressure (1.01 xx 10^(5) Pa) (o) Mass of earth (5.98 xx 10^(24)kg) (p) Mean radius of earth (6.37 xx 10^(6)m)