Vectors

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

Find the magnitude of vector \( \vec{V} = 6\hat{i} + 8\hat{j} \).

If \( \vec{A} = 2\hat{i} + 3\hat{j} \), what is the vector \( 3\vec{A} \)?

If \( \vec{A} = 4\hat{i} - \hat{j} \) and \( \vec{B} = -2\hat{i} + 5\hat{j} \), what is \( \vec{A} - \vec{B} \)?

Find the unit vector in the direction of \( \vec{A} = 3\hat{i} + 4\hat{j} \).

If \( \vec{A} = 5\hat{i} - 2\hat{j} \) and \( \vec{B} = k\hat{i} + 3\hat{j} \) are perpendicular, find \( k \).

Calculate the scalar product \( \vec{A} \cdot \vec{B} \) if \( \vec{A} = 7\hat{i} + 24\hat{j} \) and \( \vec{B} = 3\hat{i} - 4\hat{j} \).

A vector \( \vec{C} \) has magnitude 13 and makes an angle of 53° with the positive x-axis. Find its components.

If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} + k\hat{j} \) are such that \( |\vec{A} + \vec{B}| = 10 \), find \( k \).

Vectors \( \vec{A} = 3\hat{i} + 4\hat{j} \) and \( \vec{B} = x\hat{i} + 2\hat{j} \) satisfy \( \vec{A} \times \vec{B} = 10 \hat{k} \). Find \( x \).