if overrightarrow a overrightarrow b overrightarrow c hen

If $$\vec A = \vec B - \vec C,$$ then, the angle between $${\vec A}$$ and $${\vec B}$$ is

A. $${\tan ^{ - 1}}\frac{{{B^2} + {A^2} - {C^2}}}{{2AB}}$$

B. $${\sin ^{ - 1}}\frac{{{B^2} + {A^2} - {C^2}}}{{2AB}}$$

C. $${\cos ^{ - 1}}\frac{{{A^2} + {B^2} - {C^2}}}{{2AB}}$$

D. $${\sec ^{ - 1}}\frac{{{A^2} + {B^2} - {C^2}}}{{2AB}}$$

Answer : $${\cos ^{ - 1}}\frac{{{A^2} + {B^2} - {C^2}}}{{2AB}}$$

Solution :
Given, $$\vec A = \vec B - \vec C$$
$$\therefore \vec C = \vec B - \vec A$$
If $$\theta $$ is the angle between $${\vec A}$$ and $${\vec B},$$ then
$$\eqalign{ & {C^2} = {B^2} + {A^2} - 2AB\cos \theta \cr & \therefore \cos \theta = \frac{{{B^2} + {A^2} - {C^2}}}{{2AB}} \cr} $$

Releted MCQ Question on
Basic Physics >> Kinematics

Releted Question 1

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A. Due north

B. $${30^ \circ }$$ East of north

C. $${30^ \circ }$$ West of north

D. $${60^ \circ }$$ East of north

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Releted Question 2

A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-

A. 1

B. 3

C. 4

D. $$\sqrt {41} $$

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Releted Question 3

In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-

A. $$3.14 \,m/s$$

B. $$2.0 \,m/s$$

C. $$1.0 \,m/s$$

D. Zero

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Releted Question 4

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-

View Answer

If $$\vec A = \vec B - \vec C,$$ then, the angle between $${\vec A}$$ and $${\vec B}$$ is

Releted MCQ Question on
Basic Physics >> Kinematics

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-

In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-

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Kinematics

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If $$\vec A = \vec B - \vec C,$$ then, the angle between $${\vec A}$$ and $${\vec B}$$ is

Releted MCQ Question on Basic Physics >> Kinematics

A river is flowing from west to east at a speed of $$5$$ metres per minute. A man on the south bank of the river, capable of swimming at $$10$$ metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction-

A boat which has a speed of $$5 km/hr$$ in still water crosses a river of width $$1 \,km$$ along the shortest possible path in $$15 \,minutes.$$ The velocity of the river water in $$km/hr$$ is-

In $$1.0\,s,$$ a particle goes from point $$A$$ to point $$B,$$ moving in a semicircle of radius $$1.0 \,m$$ (see Figure). The magnitude of the average velocity-

A ball is dropped vertically from a height $$d$$ above the ground. It hits the ground and bounces up vertically to a height $$\frac{d}{2}.$$ Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ above the ground as-

Practice More Releted MCQ Question on Kinematics

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Kinematics