If A = i + 3j and B = 3i + j, the angle between vector A and vector B is
A) 53°.
B) 30°.
C) 45°.
D) 37°.

Question

Quizplus · Accepted Answer

The angle between two vectors A and B can be found using the dot product formula: $A \cdot B = |A||B|\cos(\theta)$, where $\theta$ is the angle between the vectors. The dot product of A and B is $A \cdot B = (i + 3j) \cdot (3i + j) = 3 + 3 = 6$. The magnitudes of A and B are $|A| = \sqrt{1^2 + 3^2} = \sqrt{10}$ and $|B| = \sqrt{3^2 + 1^2} = \sqrt{10}$. Substituting these into the formula gives $\cos(\theta) = \frac{6}{10}$, leading to $\theta \approx 53^\circ$.

If a = I + 3j and B = 3i