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Chapter 10: Q.20 (page 848)

Find the vector orthogonal to both $u=i$ and $v=2j$.

Short Answer

Expert verified

The orthogonal vector is $w=2k$.

Step by step solution

Given Information

The two vectors are $u=i$ and $v=2j$.

The result of the Cross-product of two vectors that is vector and perpendicular to both vectors.

Let the orthogonal vector be $w$.

Find the orthogonal vector

The orthogonal vector is,

$w=\begin{vmatrix}i&j&k\\1&0&0\\0&2&0\end{vmatrix}$

$w=2k$.

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Most popular questions from this chapter

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?

If u and v are vectors in $ℝ^{3}$ such that $u \cdot v = 0$ and $u \times v = 0$ , what can we conclude about u and v?

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

localid="1649405204459" role="math" $(u \times v) \cdot w and u \cdot (v \times w)$

If u, v and w are three vectors in $ℝ^{3}$ , which of the following products make sense and which do not?

localid="1649346164463" $(a) u \cdot (v \cdot w) (b) u \cdot (v \times w) (c) u \times (v \cdot w) (d) u \times (v \times w)$

Calculate each of the limits:

$\lim_{h \to 0} \frac{\frac{1}{1 + h} - 1}{h}$ .

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Find the vector orthogonal to both \(u=i\) and \(v=2j\).

Short Answer

Step by step solution

Given Information

Find the orthogonal vector

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Most popular questions from this chapter

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