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# Let the vectors be u=$-1,0,2$ , v=$0,2,-3$ , w=$2,2,3$ Calculate the following expressions a)<u,w> b) &lt;2u- 5v,3w&gt;

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## Answer to a math question Let the vectors be u=$-1,0,2$ , v=$0,2,-3$ , w=$2,2,3$ Calculate the following expressions a)<u,w> b) &lt;2u- 5v,3w&gt;

Bud
4.6
Let's calculate the given expressions involving the vectors u, v, and w: a) u • v $dot product of u and v$: u • v = $-1 * 0$ + $0 * 2$ + $2 * (-3$) = 0 - 0 - 6 = -6 b) <2u - 5v, 3w> $scalar triple product$: <2u - 5v, 3w> = $2u - 5v$ • 3w Now, calculate the individual components of 2u - 5v: 2u - 5v = $2 * (-1$, 2 * 0, 2 * 2) - $5 * 0, 5 * 2, 5 * (-3$) = $-2, 0, 4$ - $0, 10, -15$ = $-2, -10, 19$ Now, take the dot product of $-2, -10, 19$ and 3w: $-2, -10, 19$ • 3w = $-2 * 3, -10 * 3, 19 * 3$ • $3 * 2, 3 * 2, 3 * 3$ = $-6, -30, 57$ • $6, 6, 9$ Now, calculate the dot product: $-6, -30, 57$ • $6, 6, 9$ = $-6 * 6$ + $-30 * 6$ + $57 * 9$ = -36 - 180 + 513 = 297 So, the scalar triple product <2u - 5v, 3w> is 297.
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