(A) The cross product of two vectors $\vec{A}$ and $\vec{B}$ is given by $\vec{A} \times \vec{B} = AB \sin \theta \hat{n}$,where $\theta$ is the angle

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(A) The cross product of two vectors $\vec{A}$ and $\vec{B}$ is given by $\vec{A} \times \vec{B} = AB \sin \theta \hat{n}$,where $\theta$ is the angle between the vectors.If the vectors are parallel,$\theta = 0^\circ$,so $\sin 0^\circ = 0$.If the vectors are antiparallel,$\theta = 180^\circ$,so $\sin 180^\circ = 0$.In both cases,the cross product $\vec{A} \times \vec{B} = 0$.

Class 11 Physics 3-1.Vectors Multiplication of Vectors

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What is the product of two vectors if they are parallel or antiparallel?

A
The cross product is zero.
B
The dot product is zero.
C
The cross product is maximum.
D
The dot product is maximum.

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3-1.Vectors

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Multiplication of Vectors

The angle between vectors $(\overrightarrow {A} \times \overrightarrow {B})$ and $(\overrightarrow {B} \times \overrightarrow {A})$ is

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$\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{i} \times \hat{j}) = $

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Find the unit vector perpendicular to the two vectors $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$.

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The area of the parallelogram having diagonals $\vec{d_1} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{d_2} = \hat{i} - 3\hat{j} + 4\hat{k}$ is:

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If $\vec{A} = 4\hat{i} + n\hat{j} - 2\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} + \hat{k}$,find the value of $n$ such that $\vec{A} \perp \vec{B}$.

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What is the product of two vectors if they are parallel or antiparallel?

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The angle between vectors $(\overrightarrow {A} \times \overrightarrow {B})$ and $(\overrightarrow {B} \times \overrightarrow {A})$ is

$\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{i} \times \hat{j}) = $

Find the unit vector perpendicular to the two vectors $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$.

The area of the parallelogram having diagonals $\vec{d_1} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{d_2} = \hat{i} - 3\hat{j} + 4\hat{k}$ is:

If $\vec{A} = 4\hat{i} + n\hat{j} - 2\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} + \hat{k}$,find the value of $n$ such that $\vec{A} \perp \vec{B}$.

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