malgudi garden restaurant
TV3 202618()026MBS/TBS28 TURBO .
201814202444 [1][2] [3] .
3 59 (3 12))
- 1 () ABEMA24.
... .
20259868~70 1 .
.
320261 .
18 20211224 0 [5][6][7]
TV32026413 ...
Related Articles
Trending Articles
Compute $ \|\mathbf{a}\|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 $
Now compute $ \mathbf{a} \times \mathbf{b} $:
\mathbf{a} \times \mathbf{b} = \begin{vmatrix}
& -2 & 1 \\
\end{vmatrix} = \mathbf{i}(2 \cdot 1 - 3 \cdot (-2)) - \mathbf{j}(1 \cdot 1 - 3 \cdot 1) + \mathbf{k}(1 \cdot (-2) - 2 \cdot 1)
= \mathbf{i}(2 + 6) - \mathbf{j}(1 - 3) + \mathbf{k}(-2 - 2) = \langle 8, 2, -4 \rangle
14\mathbf{v} = \langle 8, 2, -4 \rangle \quad \Rightarrow \quad \mathbf{v} = \frac{1}{14} \langle 8, 2, -4 \rangle = \left\langle \frac{4}{7}, \frac{1}{7}, -\frac{2}{7} \right\rangle
Thus, the vector is $ \boxed{\left\langle \dfrac{4}{7}, \dfrac{1}{7}, -\dfrac{2}{7} \right\rangle} $.
Question: Among all roots of the polynomial $ z^6 - z^4 + z^2 - 1 = 0 $, a historian of mathematical astronomy seeks the maximum imaginary part, expressed as $ \sin \theta $ for $ 0 < \theta < \pi $. Find $ \theta $.
Solution: Consider the polynomial: