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Elodia [21]
3 years ago
5

Let r3 have the euclidean inner product. let u = (-1, 1, 1) and v = (-7, 6, 15). if ||ku + v||= 7, what is k? give the exact ans

wer using fractions if necessary. give the answers in descending order.
Mathematics
1 answer:
amm18123 years ago
3 0
Mak\mathbf u+\mathbf v=k(-1,1,1)+(-7,6,15)=(-k-7,k+6,k+15)

Recall that for a vector \mathbf x\in\mathbb R^n, we have \|\mathbf x\|=\sqrt{\mathbf x\cdot\mathbf x}. So we have

\|k\mathbf u+\mathbf v\|=\sqrt{(k\mathbf u+\mathbf v)(k\mathbf u+\mathbf v)}=7
\implies k^2\mathbf u\cdot\mathbf u+2k\mathbf u\cdot\mathbf v+\mathbf v\cdot\mathbf v=49
\implies3k^2+56k+261=0
\implies k=-9,-\dfrac{29}3
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