If the vectors A and B are such that A · B = |A| |B|, what is the angle between
Practice Questions
Q1
If the vectors A and B are such that A · B = |A| |B|, what is the angle between them?
0°
90°
180°
None of the above
Questions & Step-by-Step Solutions
If the vectors A and B are such that A · B = |A| |B|, what is the angle between them?
Step 1: Understand the dot product formula. The dot product of two vectors A and B is given by A · B = |A| |B| cos(θ), where |A| and |B| are the magnitudes of the vectors and θ is the angle between them.
Step 2: Given that A · B = |A| |B|, we can substitute this into the dot product formula. This means |A| |B| = |A| |B| cos(θ).
Step 3: Since both sides of the equation are equal, we can simplify it to cos(θ) = 1.
Step 4: The cosine of an angle is 1 when the angle θ is 0 degrees. Therefore, θ = 0°.
Dot Product of Vectors – The dot product of two vectors A and B is defined as A · B = |A| |B| cos(θ), where θ is the angle between the vectors.
Angle Between Vectors – The angle between two vectors can be determined using the relationship between their dot product and their magnitudes.
