Q. 7

Question

In Exercises 3–8, let A, B, C, D, ... , Z be points in $R^{3}$ . Simplify the given quantity.

$\vec{A B} + \vec{B C} + \vec{C A}$

Step-by-Step Solution

Verified

Answer

$\vec{A B} + \vec{B C} + \vec{C A} = 0$

1Step 1: Given

$\vec{A B} + \vec{B C} + \vec{C A}$

2Step 2: Simplify

From the law of vector addition:

$\vec{A B} + \vec{B C} + \vec{C A} = (\vec{A B} + \vec{B C}) + \vec{C A} = \vec{A C} + \vec{C A} = \vec{A C} - \vec{A C} (\vec{C A} = - \vec{A C}) = 0$

Q. 6

Q. 8

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Q. 8

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Q. 9

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