Question

Find the value of a · b.|a| when |a| = 5, |b| = 8, and the angle between a and b is 30°.

Answer 1

The value of a · b|a| when |a| = 5, |b| = 8, and the angle between a and b is 30° is found by calculating the dot product a · b = |a||b|cos(θ), which gives 20√3. Multiplying this result by |a| yields 100√3.

Step-by-step explanation:

To find the value of a · b|a| when |a| = 5, |b| = 8, and the angle between a and b is 30°, we need to use the formula for the dot product of two vectors a · b = |a||b|cos(θ), where θ is the angle between the vectors. In this case, we know the magnitudes of the vectors a and b and the angle between them.

Using the given values:

• |a| = 5
• |b| = 8
• θ = 30°

We can calculate the dot product: a · b = 5 × 8 × cos(30°). The cosine of 30° is √3/2. Thus,

a · b = 40 × (√3/2) = 20√3.

Now, since |a| = 5, we multiply this result by |a| to get:

a · b|a| = 20√3 × 5 = 100√3.

Therefore, the value of a · b|a| is 100√3.