Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 94

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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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Important Questions on Mathematical Tools in Physics

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 95

If

\vec{A} = 4 \hat{i} + n \hat{j} - 2 \hat{k}

and

\vec{B} = 2 \hat{i} + 3 \hat{j} + \hat{k},

then find the value of

n

so that

\vec{A} ⊥ \vec{B} .

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 97

Find a unit vector perpendicular to both the vectors

(2 \hat{i} + 3 \hat{j} + \hat{k})

and

(\hat{i} - \hat{j} + 2 \hat{k}) .

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 99

Area of a parallelogram, whose diagonals are

3 \hat{i} + \hat{j} - 2 \hat{k}

and

\hat{i} - 3 \hat{j} + 4 \hat{k}

will be:

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 100

If

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

and

\vec{B} = \hat{i} - \hat{j}

, the value of

(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B})

is:

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 101

Vectors

\vec{A} = \hat{i} + \hat{j} - 2 \hat{k}

and

\vec{B} = 3 \hat{i} + 3 \hat{j} - 6 \hat{k}

are :

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 102

If two vectors are given as :

\vec{A} = \hat{i} + 2 \hat{j} - \hat{k}

and

\vec{B} = - \hat{i} - \hat{j} + \hat{k}

then the vector which is not perpendicular to

(\vec{A} \times \vec{B})

is:

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 103

If a vector

2 \hat{i} + 3 \hat{j} + 8 \hat{k}

is perpendicular to the vector

4 \hat{j} - 4 \hat{i} + α \hat{k}

, then the value of

α

is

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-1>Q 104

If the angle between the vectors

\vec{A}

and

\vec{B}

is

θ

, the value of the product

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

is equal to: