Vectors

If \( \vec{A} = 3\hat{i} + 4\hat{j} \) and \( \vec{B} = \hat{i} - 2\hat{j} \), what is \( \vec{A} + \vec{B} \)?

What is the magnitude of the vector \( \vec{V} = 6\hat{i} + 8\hat{j} \)?

If \( \vec{A} = 5\hat{i} - 3\hat{j} \), what is the unit vector in the direction of \( \vec{A} \)?

Vectors \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = k\hat{i} + 6\hat{j} \) are perpendicular. Find \( k \).

If \( \vec{A} = 4\hat{i} - \hat{j} \) and \( \vec{B} = -2\hat{i} + 3\hat{j} \), find \( 3\vec{A} - 2\vec{B} \).

Two vectors \( \vec{A} \) and \( \vec{B} \) have magnitudes 5 and 12 respectively. What is the magnitude of \( \vec{A} - \vec{B} \) if they are perpendicular?

If \( \vec{A} = 7\hat{i} + 24\hat{j} \), find the angle \( \theta \) it makes with the positive x-axis.

Given \( \vec{A} = 3\hat{i} + 4\hat{j} \) and \( \vec{B} = 6\hat{i} + 8\hat{j} \), find the scalar \( k \) such that \( \vec{B} = k\vec{A} \).

If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} + k\hat{j} \) are parallel, find \( k \).