Question

1. If the angle between the vectors a and b is π/4 and | a × b | = 1, then a. b is equal to
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Answer 1

We can use the formula |a × b| = |a| |b| sin θ to solve for the magnitude of the cross product |a × b|, where θ is the angle between vectors a and b. In this case, we have |a × b| = 1 and θ = π/4, so we can write:

1 = |a| |b| sin(π/4)

Simplifying, we have:

|a| |b| = √2

Now, we need to find the dot product a · b. We know that:

a · b = |a| |b| cos θ

where θ is the angle between vectors a and b. Since we're given the angle between a and b, we can substitute θ = π/4 and use the value we found for |a| |b|:

a · b = (√2) cos(π/4) = (√2)/2

Therefore, a · b is equal to (√2)/2.

Explanation: