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Chapter 10: Q. 4 (page 800)

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

Short Answer

Expert verified

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

Step by step solution

01

Given

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

02

Simplify

From the law of vector addition,

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

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Most popular questions from this chapter

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

Find the volume of the parallelepiped determined by the vectors u, v, and w.

If u and v are nonzero vectors in $ℝ^{3}$ , why do the equations role="math" localid="1649263352081" $u \cdot (u \times v) = 0$ and $v \cdot (u \times v) = 0$ tell us that the cross product is orthogonal to both u and v?

Find a vector of length 3 that points in the direction opposite to $<1, - 2, 3>$ .

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <2, 1, - 5>$

Find the norm of the vector. $v = (0, 0, 6)$

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