To find the value of b, we can use the given information:
|a| = 7
|b| = √6
The angle between a and b is 45°.
We know that the dot product of two vectors a and b is given by:
a · b = |a| |b| cos(θ)
where θ is the angle between a and b.
In this case, we have:
a · b = 7 √6 cos(45°)
Since cos(45°) = √2 / 2, we can substitute the values:
7 √6 cos(45°) = 7 √6 (√2 / 2) = 7√12 / 2
We also know that a · b = |a| |b|, so we can set up the equation:
7√12 / 2 = 7 √6 |b|
Now, solving for |b|:
|b| = (7√12 / 2) / (7 √6)
Simplifying the expression:
|b| = √2 / 2
Therefore, the value of b is √2 / 2.