Vectors

Which of the following represents a vector quantity?

If \( \vec{A} = 3\hat{i} + 4\hat{j} \), what is the magnitude of \( \vec{A} \)?

Two vectors \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = -1\hat{i} + 4\hat{j} \) are added. What is \( \vec{A} + \vec{B} \)?

If \( \vec{A} = 5\hat{i} - 2\hat{j} \), what is the vector \( -2\vec{A} \)?

If \( \vec{A} = 4\hat{i} + 3\hat{j} \) and \( \vec{B} = k\hat{i} + 6\hat{j} \) are perpendicular, find \( k \).

Find the unit vector in the direction of \( \vec{A} = 6\hat{i} + 8\hat{j} \).

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

Vector \( \vec{C} = 7\hat{i} + y\hat{j} \) has magnitude 25. If \( y > 0 \), find \( y \).

Two vectors \( \vec{A} \) and \( \vec{B} \) satisfy \( |\vec{A}| = 5 \), \( |\vec{B}| = 12 \) and \( \vec{A} \cdot \vec{B} = 60 \). Find the angle between them.

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