(A) The magnitude of the vector $\vec{A} = \hat{i} + \hat{j}$ is given by $|\vec{A}| = \sqrt{(1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2}$.The direction $

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Magnitude = $\sqrt{2}$,Direction = $45^{\circ}$ with $x$-axis

(A) The magnitude of the vector $\vec{A} = \hat{i} + \hat{j}$ is given by $|\vec{A}| = \sqrt{(1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2}$.The direction $\theta$ with the $x$-axis is given by $\tan \theta = \frac{A_y}{A_x} = \frac{1}{1} = 1$.Therefore,$\theta = \tan^{-1}(1) = 45^{\circ}$ with the $x$-axis.

Class 11 Physics 3-1.Vectors Fundamentals of Vectors

Medium

Find the magnitude and direction of the vector $\vec{A} = \hat{i} + \hat{j}$.

A
Magnitude = $\sqrt{2}$,Direction = $45^{\circ}$ with $x$-axis
B
Magnitude = $2$,Direction = $30^{\circ}$ with $x$-axis
C
Magnitude = $\sqrt{2}$,Direction = $90^{\circ}$ with $x$-axis
D
Magnitude = $1$,Direction = $45^{\circ}$ with $x$-axis

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Two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other if one is a scalar multiple of the other,i.e.,$\vec{A} = k\vec{B}$. Which of the following pairs of vectors are parallel?

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$\vec{A}$ and $\vec{B}$ are two non-zero vectors inclined at an angle $\theta$. $\hat{a}$ and $\hat{b}$ are unit vectors along $\vec{A}$ and $\vec{B}$ respectively. The component of $\vec{A}$ in the direction of $\vec{B}$ is

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Find the magnitude and direction of the vector $\vec{A} = \hat{i} + \hat{j}$.

Similar Questions

Which of the following relations is correct?

If $A$ and $B$ are two vectors such that $|A + B| = 2|A - B|$,the angle between vectors $A$ and $B$ is:

What is the energy of an electron in a hydrogen atom in a stationary state corresponding to $n = 2$ ?

Two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other if one is a scalar multiple of the other,i.e.,$\vec{A} = k\vec{B}$. Which of the following pairs of vectors are parallel?

$\vec{A}$ and $\vec{B}$ are two non-zero vectors inclined at an angle $\theta$. $\hat{a}$ and $\hat{b}$ are unit vectors along $\vec{A}$ and $\vec{B}$ respectively. The component of $\vec{A}$ in the direction of $\vec{B}$ is

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