Chapter 9: Q. 14 (page 228)

Evaluate the dot product of the three pairs of vectors in Figure

Expert verified

$\vec{A} \cdot \vec{B} = 11.5 \vec{C} \cdot \vec{D} = - 4.6 \vec{E} \cdot \vec{F} = 0$

Step by step solution

We have

The dot product is the sum of the product of the component where this dot product is called the scalar product.

For two vector A and B and there is an angle x between then the dot product these two vectors is given by

$\vec{A} \cdot \vec{B} = A B \cos α \vec{C} \cdot \vec{D} = C D \cos α \vec{E} \cdot \vec{F} = E F \cos α$

We are given vectors by $A = 3$ and $B = 5$ and the angle is role="math" localid="1648018330260" $α = 40 °$

So,

$\vec{A} \cdot \vec{B} = A B \cos α = (3) (5) \cos 40 ° = 11.5$

The magnitude of the vector $C = 2$ and $D = 3$ and the angle is $α = 140 °$

So,

$\vec{C} \cdot \vec{D} = C D \cos α = (2) (3) \cos 140 ° = - 4.6$

The magnitude of the vector $E = 3$ and $F = 4$ and the angle is $α = 90 °$

$\vec{E} \cdot \vec{F} = E F \cos α = (3) (4) \cos 90 ° = 0$

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