I know that impulse is the change in linear momentum. Is the direction of impulse always along the change in momentum vector? Please explain.


You have already said you are aware that the impulse $\mathbf J$ is the change in linear momentum $\Delta\mathbf p$, so we have $$\mathbf J\equiv\Delta\mathbf p$$

This is a vector equation. When two vectors are equal they must have the same magnitude and direction.

In general, if we have two vectors $\mathbf a$ and $\mathbf b$ that are equal, then their components must be equal (let's assume we are working with 2D vectors here) $$a_x=b_x$$ $$a_y=b_y$$

So looking at the magnitude of $\mathbf a$: $$||\mathbf a||=\sqrt{a_x^2+a_y^2}=\sqrt{b_x^2+b_y^2}=||\mathbf b||$$

And looking at the direction of $\mathbf a$: $$\theta_a=\tan^{-1}\left(\frac{a_y}{a_x}\right)=\tan^{-1}\left(\frac{b_y}{b_x}\right)=\theta_b$$

Therefore, two vectors that are equal must have the same magnitude and direction


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