Find the Vector Projv U $\frac { 19 } { 169 } \mathbf { i } + \frac { 19 } { 169 } \mathbf { j } + \frac { 19 } { 169 } \mathbf { k }$

question 161

Multiple Choice

Find the vector projv u.
-v = i + j + k, u = 3i + 4j + 12k

• A) \(\frac { 19 } { 169 } \mathbf { i } + \frac { 19 } { 169 } \mathbf { j } + \frac { 19 } { 169 } \mathbf { k }\)
• B) \(\frac { 19 } { 13 } \mathbf { i } + \frac { 19 } { 13 } \mathbf { j } + \frac { 19 } { 13 } \mathbf { k }\)
• C) \(\frac { 20 } { 3 } \mathbf { i } + \frac { 20 } { 3 } \mathbf { j } + \frac { 20 } { 3 } \mathbf { k }\)
• D) \(\frac { 19 } { 3 } \mathbf { i } + \frac { 19 } { 3 } \mathbf { j } + \frac { 19 } { 3 } \mathbf { k }\)

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Definitions:

Long-Run Average Cost

The average cost per unit of output where all inputs, including capital, are variable over time, reflecting economies or diseconomies of scale.

Plant Size

The capacity or physical extent of a manufacturing facility, which influences its production capabilities, economies of scale, and operational efficiency.

ATC

ATC, or Average Total Cost, is the per-unit cost of production, calculated by dividing the total cost by the quantity of output produced, comprising both fixed and variable costs.

Marginal Cost

The cost of producing one additional unit of a good or service, considered crucial in determining production levels and pricing decisions.