Find a Nonzero Vector Orthogonal to the Plane Through the Points

question 43

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

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Definitions:

Value Marginal Product

The additional revenue generated by employing one more unit of a factor of production, such as labor or capital.

Skilled Labor

Workers who have specialized training, education, or experience that is valuable for specific jobs, industries, or tasks.

Unskilled Labor

Workforce sector comprising individuals without specialized training or qualifications, often employed in tasks that require manual efforts.

Marginal Productivity

The additional output that is produced by employing one more unit of a factor of production, holding all other factors constant.