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Chapter 10: Q 34. (page 801)

Find the norm of the vector. $v = (\frac{1}{2}, \frac{1}{3}, \frac{1}{4})$

Short Answer

Expert verified

The norm of the vector $v = (\frac{1}{2}, \frac{1}{3}, \frac{1}{4})$ is $\sqrt{\frac{61}{144}}$ .

Step by step solution

01

Step 1. Given information .

We have given vector $v = (\frac{1}{2}, \frac{1}{3}, \frac{1}{4})$

02

Step 2. Find the norm of the vector.

$||v|| = \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{{(\frac{1}{2})}^{2} + {(\frac{1}{3})}^{2} + {(\frac{1}{4})}^{2}} = \sqrt{\frac{1}{4} + \frac{1}{9} + \frac{1}{16}} = \sqrt{\frac{36 + 16 + 9}{144}} = \sqrt{\frac{61}{144}}$

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Most popular questions from this chapter

Prove the first part of Theorem $1.31$ (a): If $k > 0$ , then $\lim_{x \to \infty} x^{k} = \infty$ . (Hint: Given $M > 0$ , choose $N = M^{1 / k}$ . Then show that for $x > N$ it must follow that $x^{k} > M$ .)

What is the definition of the cross product?

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

$u \times v and v \times u$

How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors $u = (u_{1}, u_{2}, u_{3}) and v = (v_{1}, v_{2}, v_{3})$ ?

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.

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