Find a Nonzero Vector Orthogonal to the Plane Through the Points

question 4

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

---

Definitions:

Beta

A measure of the volatility, or systematic risk, of a security or portfolio compared to the market as a whole.

Factor Portfolio

A portfolio constructed to have a high sensitivity to certain risk factors, aiming to achieve specific investment outcomes related to those factors.

Well-diversified Portfolio

An investment portfolio spread across different assets to reduce exposure to risk associated with any single investment.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, commonly used in finance to assess the volatility of an investment.