Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 68

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The rectangular components of a vector are $(2, 2)$ . The corresponding rectangular components of another vector are $(1, \sqrt{3}) .$ Find the angle between the two vectors(in degrees).

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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 69

The

x

and

y

components of a force are

2 N

and

- 3 N

. The force is ..... (in

N

)

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 70

The vector joining the points

A (1, 1, - 1)

and

B (2, - 3, 4)

and pointing from

A

to

B

is

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 71

If

\vec{A} = \hat{i} + \hat{j} + \hat{k}

and

\vec{B} = 2 \hat{i} + \hat{j}

, then find the magnitude of

(\vec{A} \cdot \vec{B}) \times {(\vec{A} \times \vec{B})}^{2}

.

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 72

If $| \vec{A} | = 4, | \vec{B} | = 3$ and $θ = 60 °$ in the figure, find $\frac{{(| \vec{A} \times \vec{B} |)}^{2}}{(\vec{A} \cdot \vec{B})}$ .

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 73

Three non-zero vectors

\vec{A}, \vec{B}

and

\vec{C}

satisfy the relation

\vec{A} \cdot \vec{B} = 0

and

\vec{A} \cdot \vec{C} = 0

. Then,

\vec{A}

can be parallel to:

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 74

The magnitude of scalar product of two vectors is

8

and that of vector product is

8 \sqrt{3}

. The angle between them is

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 75

Vector

\vec{A}

points

N - E

and its magnitude is

3 kg m s^{- 1}

. It is multiplied by the scalar

λ

such that,

λ = - 4

second

. Find the direction and magnitude of the new vector quantity. Does it represent the same physical quantity or not?

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Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 1>Q 76

A force of

30 N

is inclined at an angle

θ °

to the horizontal. If its vertical component is

18 N

, and the horizontal component is

x N

. What is the value of

x + 2 θ

?