Question

Compute $u \cdot v$, $\overline{w}^T u$, $\overline{w} \cdot \overline{v}$, $u \cdot (v + w)$, and $\overline{v}^T (\overline{k}w)$ using Formula (5) and parts (a), (b), (c), (d) of Theorem 5.3.3 where applicable. $u = (i, 6i, 6)$, $v = (7, -6i, 1 + i)$, $w = (6 - i, 6i, 7 + 6i)$, $k = 6i$ $u \cdot v = i - 30$ $\overline{w}^T u = 77 - 30i$ $\overline{w} \cdot \overline{v} = 19 + 8i$ $u \cdot (v + w) = 47 - 29i$ $\overline{v}^T (\overline{k}w) = 36 - 474i$

          Compute $u \cdot v$, $\overline{w}^T u$, $\overline{w} \cdot \overline{v}$, $u \cdot (v + w)$, and $\overline{v}^T (\overline{k}w)$ using Formula (5) and parts (a), (b), (c), (d) of Theorem 5.3.3 where applicable.
$u = (i, 6i, 6)$, $v = (7, -6i, 1 + i)$, $w = (6 - i, 6i, 7 + 6i)$, $k = 6i$
$u \cdot v = i - 30$
$\overline{w}^T u = 77 - 30i$
$\overline{w} \cdot \overline{v} = 19 + 8i$
$u \cdot (v + w) = 47 - 29i$
$\overline{v}^T (\overline{k}w) = 36 - 474i$

Compute u · v, w^T u, w·v, u · (v + w), and v^T (kw) using Formula (5) and parts (a), (b), (c), (d) of Theorem 5.3.3 where applicable.
u = (i, 6i, 6), v = (7, -6i, 1 + i), w = (6 - i, 6i, 7 + 6i), k = 6i
u · v = i - 30
w^T u = 77 - 30i
w·v = 19 + 8i
u · (v + w) = 47 - 29i
v^T (kw) = 36 - 474i

Added by Richard S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Brian Sipko

08/16/2021

Step 1

v = u1v1 + u2v2 + u3v3, where u = (u1, u2, u3) and v = (v1, v2, v3), we can compute u.v as follows: u.v = (i)(7) + (6i)(-6i) + (6)(1+i) u.v = 7i - 36 + 6 + 6i u.v = 12i - 30 Show more…

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Compute Compute u.v, wTu, w.v, u.(v+ w), and vT(kw) using Formula (5) and parts (a), (b), (c), (d) of Theorem 5.3.3 where applicable. u=i, 6i, 6), v=7, -6i, 1+i), w=6-i, 6i, 7+6i, k=6i u.v= i-30 wTu= 77 - 30i w.v= 19+8i u.(v+w)= 47-29i vT(kw)= 36-474i