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Chapter 10: Q 2 (page 847)

Fill in the blanks:
For any vectors $u = <u_{1}, u_{2}, u_{3}>, v = <v_{1}, v_{2}, v_{3}>$ , $u . v =__________$

Short Answer

Expert verified

The required answer is $u_{1} v_{1} + u_{2} v_{2} + u_{3} v_{3}$

Step by step solution

01

Given information

Two vectors $u = <u_{1}, u_{2}, u_{3}>, v = <v_{1}, v_{2}, v_{3}>$

02

Filling in the blank

As per the dot product formula:

$u . v = u_{1} v_{1} + u_{2} v_{2} + u_{3} v_{3}$

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Most popular questions from this chapter

If u and v are vectors in ${鈩�}^{3}$ such that $u 路 v = 0$ and $u 脳 v = 0$ , what can we conclude about u and v?

In Exercises 30鈥�35 compute the indicated quantities when

$u = (鈭� 3, 1, 鈭� 4), v = (2, 0, 5), and w = (1, 3, 13)$

$u 脳 v and v 脳 u$

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

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

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