Question

define scalar product of two vectors. ​

Answer 1

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mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number.

Answer 2

Answer:

By definition of the scalar or dot product of vectors, we know that

a⃗ .b⃗  = |a⃗ | |b⃗ | cosθ

where θ is the angle between a⃗  and b⃗ . In this question, we have,

|a⃗ | = 3–√, |b⃗ | = 2, and a⃗ .b⃗  = 6–√

Replacing these values in the formula, we get

a⃗ .b⃗  = |a⃗ | |b⃗ | cosθ

⟺ 6–√ = 3–√ x 2 x cosθ

⟺ 3–√ x 2–√ = 3–√ x 2–√ x 2–√ x cosθ

Cancelling the common terms on both sides, we get

1 = 2–√ x cosθ

Or, cosθ = 12√

Therefore, θ = π4

Hence, the angle between the vectors a⃗  and b⃗  is π4.

Explanation: