Question

Vectors v and w are sides of an equilateral triangle whose sides have length 3. Compute

v · w.

Answer 1

To find the dot product of two sides of an equilateral triangle with side length 3, we use the angle between the vectors, which is 60 degrees. Using the formula v · w = |v||w|cos(θ), the dot product is calculated as 4.5.

Step-by-step explanation:

To compute the dot product v · w of two vectors that are sides of an equilateral triangle, we need to consider the angle between the vectors and the magnitude of each vector.

In an equilateral triangle, all the angles are 60 degrees. The dot product is calculated using the formula v · w = |v||w|cos(θ), where θ is the angle between the vectors v and w, and |v| and |w| are the magnitudes of the vectors. In our case, since the vectors form the sides of an equilateral triangle, we have:

|v| = |w| = 3

θ = 60 degrees

Thus, the dot product is:

v · w = 3 × 3 × cos(60°) = 9 × (1/2) = 4.5.

Answer 2

4.5

Step-by-step explanation:

The length of the vectors v and w is 3, and the inner product is defined as:

|v|*|w| cos α

So, for an equilateral triangle, α=60° and cos 60° = 1/2

3*3*1/2 = 4.5