For which following condition, will the dot product of two vectors be zero?
a) If the angle between them is 90°.
b) If the angle between them is 0°.
c) If the angle between them is 180°
d) If the vectors have the same magnitude.
Anyone know what the answer is?
Count Iblis, it always is more productive to actually supply at least somewhat detailed explanations instead of just handing over the correct answer.
The answer is:
a) If the angle between them is 90°.
When the angle between two vectors is 90°, the dot product of the vectors will be zero.
To determine the condition for which the dot product of two vectors will be zero, we can analyze the properties of the dot product.
The dot product of two vectors can be calculated using the formula:
A · B = |A| |B| cos(θ)
where A represents the magnitude of vector A, B represents the magnitude of vector B, and θ represents the angle between the two vectors.
Given the options:
a) If the angle between them is 90°:
If the angle between two vectors is 90°, then the cosine of 90° is zero. This means that the dot product will be zero regardless of the magnitudes of the vectors. Therefore, option (a) is correct.
b) If the angle between them is 0°:
If the angle between two vectors is 0°, then the cosine of 0° is 1. This means that the dot product will only be zero if at least one of the vectors has a magnitude of zero. Therefore, this option is not correct.
c) If the angle between them is 180°:
If the angle between two vectors is 180°, then the cosine of 180° is -1. This means that the dot product will be zero only if one vector has a magnitude of zero or if both vectors have the same magnitude. Therefore, this option is not correct.
d) If the vectors have the same magnitude:
If the vectors have the same magnitude, then the cos(θ) term becomes either 1 or -1 depending on whether the angle between them is 0° or 180° respectively. Therefore, the dot product will not always be zero, so this option is not correct.
Considering the explanations above, the correct answer is option (a) - If the angle between the vectors is 90°.