Question

9 given two vectors

a⃗ =4i^−3j^+2k^

,

b⃗ =i^+2j^−k^

, calculate

a⃗ ⋅b⃗

2

-4

-2

4

Answer 1

Answer on Question 56256, Physics, Mechanics, Relativity

Question:

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

a) 2

b) -4

c) -2

d) 4

Solution:

By the definition of the dot product of two vectors $\vec{a}$ and $\vec{b}$ we have:

$$\vec{a} \cdot \vec{b} = a_1 b_1 + a_2 b_2 + a_3 b_3 = (4\hat{i} - 3\hat{j} + 2\hat{k}) \cdot (\hat{i} + 2\hat{j} - \hat{k}) = 4 \cdot 1 + (-3) \cdot 2 + 2 \cdot (-1) = 4 - 6 - 2 = -4.$$

Answer:

b) -4

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