Question:
If both x and y components of a vector are equal, its angle with x-axis is
If both x and y components of a vector are equal, its angle with x-axis is
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When the components are equal, the vector bisects the angle between the axes. Since the total angle between the x and y axes is $90^{\circ}$, half of that is exactly $45^{\circ}$.
Updated On: Apr 24, 2026
- $30^{\circ}$
- $45^{\circ}$
- $60^{\circ}$
- $90^{\circ}$
- $0^{\circ}$
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The Correct Option is B
Solution and Explanation
Concept:
Physics - Vector Components and Direction.
The direction of a vector $\vec{A} = A_x\hat{i} + A_y\hat{j}$ with respect to the positive x-axis is given by $\tan\theta = \frac{A_y}{A_x}$.
Step 1: Identify the given condition.
The problem states that the x-component ($A_x$) and the y-component ($A_y$) of the vector are equal. $$ A_x = A_y $$
Step 2: Apply the tangent formula for direction.
Substitute the equality into the direction formula: $$ \tan\theta = \frac{A_y}{A_x} $$ $$ \tan\theta = \frac{A_x}{A_x} = 1 $$
Step 3: Calculate the angle.
Find the angle whose tangent is 1: $$ \theta = \tan^{-1}(1) $$ $$ \theta = 45^{\circ} $$
Physics - Vector Components and Direction.
The direction of a vector $\vec{A} = A_x\hat{i} + A_y\hat{j}$ with respect to the positive x-axis is given by $\tan\theta = \frac{A_y}{A_x}$.
Step 1: Identify the given condition.
The problem states that the x-component ($A_x$) and the y-component ($A_y$) of the vector are equal. $$ A_x = A_y $$
Step 2: Apply the tangent formula for direction.
Substitute the equality into the direction formula: $$ \tan\theta = \frac{A_y}{A_x} $$ $$ \tan\theta = \frac{A_x}{A_x} = 1 $$
Step 3: Calculate the angle.
Find the angle whose tangent is 1: $$ \theta = \tan^{-1}(1) $$ $$ \theta = 45^{\circ} $$
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