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Home » Solution: Two vectors are orthogonal if their dot product is zero. Compute: - 500apps

Solution: Two vectors are orthogonal if their dot product is zero. Compute: - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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& 2 & 3 \\
\end{vmatrix} = \langle 2v_3 - 3v_2, 3v_1 - v_3, v_2 - 2v_1 \rangle =...
This yields the system:
2v_3 - 3v_2 = 4, \quad 3v_1 - v_3 = 5, \quad v_2 - 2v_1 = 6.
From the third equation, $v_2 = 6 + 2v_1$. Substituting into the first...
2v_3 - 3(6 + 2v_1) = 4 \implies 2v_3 - 18 - 6v_1 = 4 \implies 2v_3 = 2...
Substitute $v_3$ into the second equation:
3v_1 - (11 + 3v_1) = 5 \implies -11 = 5, \text{ which is a contradicti...
However, the condition $\mathbf{v} \cdot \mathbf{a} = 0$ implies $v_1...
v_1 + 2(6 + 2v_1) + 3(11 + 3v_1) = 0 \implies v_1 + 12 + 4v_1 + 33 + 9...

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