The dot product between two vectors is negative when the angle between the vectors is?

In mathematics and in science, vectors are quantities with both direction and magnitude. Vectors help to represent different quantities in the same expression simultaneously.

Answer: The dot product between two vectors is negative when the angle between the vectors is between 90 degrees and 270 degrees, excluding 90 and 270 degrees.

Let's solve this question step by step using the dot product formula.

Explanation:

We know, the dot product of two vectors a and b is,

a.b = |a| |b| cosα

Where,

a represents vector a and

b represents vector b

|a| is the magnitude of vector a

|b| is the magnitude of vector b

The sign dot product depends on the value of cosα. cos is negative in second and third quadrant.

For example,

α = 180°

cos(180°) = -1

Now,

a.b = |a| |b| cos(180°)

a.b = |a| |b| (-1)

a.b = -ab

Hence, the dot product between two vectors is negative when the angle between the vectors is between 90 degrees and 270 degrees, excluding 90 and 270 degrees.