Question

If \(\vec{a}\) and \(\vec{b}\) are real vectors, then saying the dot product is commutative is to say: ? \(\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}\) ? \((\vec{a} \cdot \vec{b}) \cdot \vec{c} = \vec{a} \cdot (\vec{b} \cdot \vec{c})\) ? \(\vec{a} \cdot (\vec{b} + \vec{c}) = \vec{a} \cdot \vec{b} + \vec{a} \cdot \vec{c}\) ? \((c_1\vec{a}) \cdot (c_2\vec{b}) = c_1c_2\vec{a}\cdot\vec{b}\)

          If \(\vec{a}\) and \(\vec{b}\) are real vectors, then saying the dot product is commutative is to say:

? \(\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}\)

? \((\vec{a} \cdot \vec{b}) \cdot \vec{c} = \vec{a} \cdot (\vec{b} \cdot \vec{c})\)

? \(\vec{a} \cdot (\vec{b} + \vec{c}) = \vec{a} \cdot \vec{b} + \vec{a} \cdot \vec{c}\)

? \((c_1\vec{a}) \cdot (c_2\vec{b}) = c_1c_2\vec{a}\cdot\vec{b}\)

If a⃗ and b⃗ are real vectors, then saying the dot product is commutative is to say:

? a⃗·b⃗ = b⃗·a⃗

? (a⃗·b⃗) ·c⃗ = a⃗· (b⃗·c⃗)

? a⃗· (b⃗ + c⃗) = a⃗·b⃗ + a⃗·c⃗

? (c1a⃗) · (c2b⃗) = c1c2a⃗·b⃗

Added by Tanner P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nishant Kumar

05/18/2022

Step 1

Step 1: The dot product of two vectors \vec{a} and \vec{b} is defined as \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| cos(theta), where theta is the angle between the two vectors. Show more…

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If vec{a} and vec{b} are real vectors, then saying the dot product is commutative is to say: vec{a} cdot vec{b} = vec{b} cdot vec{a} (vec{a} cdot vec{b}) cdot vec{c}^{a} = vec{a} cdot ((vec{b}) cdot vec{c}^{x}) frac{a^{2}}{} cdot (vec{b} + vec{c}) = vec{a} cdot vec{b} + vec{a} cdot vec{c} (c_{1}a^{a}) cdot (c_{2}b^{i}) = c_{1}c_{2}a^{2}b 3d arreavectorhenying the dot product is commutative is to say 2.2-220 O(a(c=cca