Question

Given two vectors a=4i^-3j^+2k^, b=i^+2j^-k^ calculate a.b

Answer 1

Answer on Question # 59234 – Physics – Mechanics | Relativity

Given two vectors $\vec{a} = 4\vec{i} - 3\vec{j} + 2\vec{k}$ ; $\vec{b} = \vec{i} + 2\vec{j} - \vec{k}$ . Calculate $\vec{a} \cdot \vec{b}$ .

**Solution:**

The dot product of the two vectors:

$$\vec {a} \cdot \vec {b} = a _ {x} \cdot b _ {x} + a _ {y} \cdot b _ {y} + a _ {z} \cdot b _ {z} = 4 \times 1 + (- 3) \times 2 + 2 \times (- 1) = 4 - 6 - 2 = - 4.$$

**Answer:** $\vec{a} \cdot \vec{b} = -4$ .

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