Vectors A → , B → and C → are shown in the figure. Find the angle between (i) A → and B → , (ii) A → and C → , and (iii) B → and C → .

(i) Angle between A → and B → , The angle between two vectors is the smallest angle between the lines when either two tails or two heads are joined. So here, the angle between two heads is 45 ° + 60 ° = 105 ° . (ii) Angle between A → and C → , The angle between two vectors is the smallest angle between the lines when either two tails or two heads are joined. So here, the angle between two heads is 30 ° + 90 ° + 30 ° = 150 ° . (iii) Angle between B → and C → , The angle between two vectors is the smallest angle between the lines when either two tails or two heads are joined. Angle between heads of B → and C → is 45 ° + 60 ° = 105 ° .

Two vectors a → and b → , inclined at an angle θ with respect to each other, have a resultant c → , which makes an angle β with a → . If the directions of a → and b → are interchanged, then, the resultant will have the same,

magnitude as well as direction.

neither magnitude nor direction.

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$I = \int_{0}^{π} \sin (θ + ϕ) d θ$ , where $ϕ$ is a non-zero constant. Then the value of $I$ ,

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Important Questions on Mathematical Tools in Physics

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 51

Vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are shown in the figure. Find the angle between (i) $\vec{A}$ and $\vec{B}$ , (ii) $\vec{A}$ and $\vec{C}$ , and (iii) $\vec{B}$ and $\vec{C}$ .

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 52

The forces, each numerically equal to

5 N

are acting as shown in the figure. Find the angle between the forces(in degrees).

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 53

Rain is falling vertically downwards with a speed of

5 m s^{- 1}

. If unit vector along upward direction is defined as

\hat{j}

, then representation of the velocity of rain in vector form is

x \hat{j}

. Find

x

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 54

A vector of magnitude

30 m

and direction eastwards is added with another vector of magnitude

40 m

and direction northwards. If the magnitude of the resultant is

x m

and the angle made by the direction of the resultant with the east is

θ °

, Find the value of

2 x + θ

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 55

Two vectors

\vec{a}

and

\vec{b}

, inclined at an angle

θ

with respect to each other, have a resultant

\vec{c}

, which makes an angle

β

with

\vec{a}

. If the directions of

\vec{a}

and

\vec{b}

are interchanged, then, the resultant will have the same,

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 56

Two vectors

\vec{A}

and

\vec{B}

lie in a plane. Another vector

\vec{C}

lies outside this plane (this plane is not parallel to the plane containing

\vec{A}

and

\vec{B}

). The resultant

\vec{A} + \vec{B} + \vec{C}

of these three vectors

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 57

The vector sum of the forces of

10 N

and

6 N

can be,

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 58

A set of vectors taken in a given order gives a closed polygon. Then, the resultant of these vectors is a

I=∫0πsinθ+ϕdθ, where ϕ is a non-zero constant. Then the value of I,

Important Questions on Mathematical Tools in Physics

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$I = \int_{0}^{π} \sin (θ + ϕ) d θ$ , where $ϕ$ is a non-zero constant. Then the value of $I$ ,