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Chapter 10: Q 10 (page 848)

Describe the mathematical expression $u . v$

Short Answer

Expert verified

It represents the dot product of two vectors.

Step by step solution

Given information

Mathematical expression $u . v$

Describing the mathematical expression

The expression represents the dot product of two vectors.

Let $u = <u_{1}, u_{2}>, v = <v_{1}, v_{2}>, then u . v = u_{1} v_{1} + u_{2} v_{2}$

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Most popular questions from this chapter

Find $u + v a n d u - v$ also sketch $u, v, u + v, u - v$

role="math" localid="1649603943715" $u = (3, 6, 11) a n d v = (1, - 2, 3)$

Find a vector in the direction of $<8, - 7, 2>$ and with magnitude 2.

Find a vector in the direction of $<9, 0, - 6>$ and with magnitude 7.

Consider the sequence of sums $\frac{1}{3}, \frac{1}{3} + \frac{1}{9}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81}, 鈥�$

(a) What happens to the terms of this sequence of sums as k gets larger and larger?

(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).

Find $u + v$ and $u - v$ . Also, sketch $u, v, u + v$ and $u - v$ .

role="math" localid="1649572653771" $u = (2, - 6), v = (6, 2)$ ,

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Describe the mathematical expressionu.v

Short Answer

Step by step solution

Given information

Describing the mathematical expression

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Most popular questions from this chapter

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Describe the mathematical expression $u . v$