Vectors

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

The magnitude of vector \( \vec{V} = 5\hat{i} + 12\hat{j} \) is:

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

If \( \vec{A} = 6\hat{i} + 8\hat{j} \), what is the vector \( 3\vec{A} \)?

Vectors \( \vec{A} = 4\hat{i} + 3\hat{j} \) and \( \vec{B} = -3\hat{i} + 4\hat{j} \) are:

If \( \vec{A} = 7\hat{i} + 24\hat{j} \), what is the magnitude of the unit vector in the direction of \( \vec{A} \)?

If \( \vec{A} = 3\hat{i} + 4\hat{j} \), find the vector \( \vec{B} \) such that \( \vec{A} + \vec{B} = \vec{0} \).

If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 5\hat{i} + k\hat{j} \), and \( \vec{A} \cdot \vec{B} = 0 \), find \( k \).

Two vectors \( \vec{A} \) and \( \vec{B} \) have magnitudes 5 and 12 respectively. If the magnitude of \( \vec{A} + \vec{B} \) is 13, what is the angle between them?

If \( \vec{A} = a\hat{i} + b\hat{j} \) is a unit vector, which of the following is true?