Find a Nonzero Vector Orthogonal to the Plane Through the Points

question 55

Multiple Choice

Find a nonzero vector orthogonal to the plane through the points $P , Q$ , and $R$ . $P ( 1,0,0 ) , Q ( 7,8,0 ) , R ( 0,8,1 )$

• A) \(\mathbf { i } - 7 \mathbf { j } + 8 \mathbf { k }\)
• B) \(- 7 \mathbf { i } + \mathbf { j } + 8 \mathbf { k }\)
• C) \(\mathbf { i } - 8 \mathbf { j } + 7 \mathbf { k }\)
• D) \(8 \mathbf { i } - 6 \mathbf { j } + 56 \mathbf { k }\)
• E) None of these

---

Definitions:

Factoring

The process of breaking down an expression into simpler terms that, when multiplied together, produce the original expression.

Square Root Property

The square root property states that if \(x^2 = a\), then \(x = \pm\sqrt{a}\), assuming \(a\) is non-negative.

Complex Solutions

Solutions to equations that involve complex numbers, which include a real component and an imaginary component.

Real Solutions

Real solutions refer to the solutions of an equation that are real numbers, as opposed to complex or imaginary numbers.