How to Find ab if a = 3, b = 14, and the Angle Between a and b is 45 degrees?

To find the product of a and b, denoted as ab, with the values given, we can use the properties of vectors.

Here, we have:

• a = 3
• b = 14
• Angle between a and b = 45 degrees

The formula to find the product of two vectors considering the angle between them is:

ab = |a| |b| cos(θ)

In this scenario:

• |a| = 3
• |b| = 14
• θ = 45 degrees

Now, we plug in the values:

cos(45 degrees) = √2/2 (approximately 0.7071)

So, we have:

ab = 3 * 14 * (√2/2)

This simplifies to:

ab = 42 * (√2/2) = 21√2

Consequently, the result of ab is 21√2 or approximately 29.7.