A force $\stackrel{\to }{\mathrm{F}}=6\stackrel{^}{\mathrm{i}}-8\stackrel{^}{\mathrm{j}}+10\stackrel{^}{\mathrm{k}}$ Newton produces acceleration  in a body. The mass of the body is (in kg)

(A)  $6\stackrel{^}{\mathrm{i}}-8\stackrel{^}{\mathrm{j}}+10\stackrel{^}{\mathrm{k}}$

(B)  $100$

(C)  $10\sqrt{2}$

(D)  $10$

Concept Questions :-

Resultant of Vectors
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angle between $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ is

(A)  $120°$

(B)  $90°$

(C)  $60°$

(D)  $30°$

Concept Questions :-

Scalar Product
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Given the vectors

Find the angle between

(A)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

(B)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

(C)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{\sqrt{2}}{3}\right)$

(D)  none of these

Concept Questions :-

Scalar Product
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If vector  and $\stackrel{\to }{\mathrm{R}}$ have magnitude 5, 12 and 13 units and $\stackrel{\to }{\mathrm{P}}+\stackrel{\to }{\mathrm{Q}}=\stackrel{\to }{\mathrm{R}}$ the angle between $\stackrel{\to }{\mathrm{Q}}$ and $\stackrel{\to }{\mathrm{R}}$ is -

(A)

(B)

(C)

(D)

Concept Questions :-

Resultant of Vectors
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The vector having a magnitude of 10 and perpendicular to the vector $3\stackrel{^}{\mathrm{i}}-4\stackrel{^}{\mathrm{j}}$ is

1. $4\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}$

2.

3. $8\stackrel{^}{\mathrm{i}}+6\stackrel{^}{\mathrm{j}}$

4.  $8\stackrel{^}{\mathrm{i}}-6\stackrel{^}{\mathrm{j}}$

Concept Questions :-

Scalar Product
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A force $\stackrel{\to }{\mathrm{F}}=3\stackrel{^}{\mathrm{i}}+\mathrm{c}\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$ acting on a particle causes a displacement $\stackrel{\to }{\mathrm{d}}=-4\stackrel{^}{\mathrm{i}}+2\stackrel{^}{\mathrm{j}}+3\stackrel{^}{\mathrm{k}}$. If the work done is 6J then the value of 'c' is

(A)  12

(B)  0

(C)  6

(D)  1

Concept Questions :-

Scalar Product
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A particle moving along a straight line according to the law $\mathrm{x}=\mathrm{At}+{\mathrm{Bt}}^{2}+{\mathrm{Ct}}^{3}$, where x is its position measured from a fixed point on the line and t is the time elapsed till it reaches position x after starting from the fixed point. Here A, B and C are positive constants.

(A)  Its velocity at t=0 is A

(B)  Its acceleration at t=0 is B

(C)  Its velocity at t=0 is B

(D)  Its acceleration at t=0 is C

Concept Questions :-

Differentiation
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If the velocity of a particle moving on x-axis is given by $\mathrm{v}=3{\mathrm{t}}^{2}-12\mathrm{t}+6$. At which time is the acceleration of particle zero?

(A)  $2$ sec

(B)  $2+\sqrt{2}$ sec

(C)  $2-\sqrt{2}$ sec

(D)  zero

Concept Questions :-

Differentiation
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Momentum of a body moving in a straight line is . Find the force acting on a body at t=2 sec

(A)  6 N

(B)  8 N

(C)  4 N

(D)  2 N

Concept Questions :-

Differentiation
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A particle moves along straight line such that at time t its position from a fixed point O on the line is $\mathrm{x}=3{\mathrm{t}}^{2}-2$. The velocity of the particle when t=2 is:

(A)

(B)

(C)

(D)  $0$

Concept Questions :-

Differentiation
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