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Q. 23

Expert-verifiedFound in: Page 824

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

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

$u\times w\mathrm{and}w\times u$

The value of $u\times w=23i+4j+14k$ and $w\times u=-23i-4j-14k$.

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

We have to find the value of $u\times w\mathrm{and}w\times u$

The value of vectors $u=(2,1,-3),w=(-2,6,5)$

The cross product of $u\times w=\mathrm{det}\left[\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ 2& 1& -3\\ -2& 6& 5\end{array}\right]$

$u\times w=\mathrm{det}\left[\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ 2& 1& -3\\ -2& 6& 5\end{array}\right]\phantom{\rule{0ex}{0ex}}u\times w=\left(\right(1\left)\right(5)-(-3\left)\right(6\left)\right)i+\left(\right(2\left)\right(5)-(-2\left)\right(-3\left)\right)j+\left(\right(2\left)\right(6)-(1\left)\right(-2\left)\right)k\phantom{\rule{0ex}{0ex}}u\times w=(5+18)i+(10-6)j+(12+2)k\phantom{\rule{0ex}{0ex}}u\times w=23i+4j+14k$

The value of vectors $w=(-2,6,5)\mathrm{and}\mathrm{u}=(2,1,-3)$

The cross product of $w\times u=\mathrm{det}\left[\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ -2& 6& 5\\ 2& 1& -3\end{array}\right]$

$w\times u=\mathrm{det}\left[\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ -2& 6& 5\\ 2& 1& -3\end{array}\right]\phantom{\rule{0ex}{0ex}}w\times u=\left(\right(6\left)\right(-3)-(5\left)\right(1\left)\right)i+\left(\right(-2\left)\right(-3)-(5\left)\right(2\left)\right)j+\left(\right(-2\left)\right(1)-(6\left)\right(2\left)\right)k\phantom{\rule{0ex}{0ex}}w\times u=(-18-5)i+(6-10)j+(-2-12)k\phantom{\rule{0ex}{0ex}}w\times u=-23i-4j-14k$

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