Find a Vector-Valued Function Whose Graph Is the Plane $x + y + z = 4 \text {. }$

question 55

Multiple Choice

Find a vector-valued function whose graph is the plane $x + y + z = 4 \text {. }$

• A) \(\mathbf { r } ( u , v ) = u \mathbf { i } - v \mathbf { j } - ( 4 - u - v ) \mathbf { k }\)
• B) \(\mathbf { r } ( u , v ) = u \mathbf { i } + v \mathbf { j } + ( 4 - u - v ) \mathbf { k }\)
• C) \(\mathbf { r } ( u , v ) = u \mathbf { i } + v \mathbf { j } + ( 4 + u + v ) \mathbf { k }\)
• D) \(\mathbf { r } ( u , v ) = u \mathbf { i } + v \mathbf { j } - ( 4 + u + v ) \mathbf { k }\)
• E) \(\mathbf { r } ( u , v ) = - u \mathbf { i } - v \mathbf { j } + ( 4 - u - v ) \mathbf { k }\)

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Definitions:

North America

A continent entirely within the Northern Hemisphere and almost all within the Western Hemisphere; it is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the east, the Pacific Ocean to the west, and South America and the Caribbean Sea to the southeast.

South Pole

The southernmost point on the Earth's surface, depicted as the point where the Earth's axis of rotation intersects its surface in the Antarctic.

Antarctica

The Earth's southernmost continent, containing the geographic South Pole, noted for its vast ice sheets and extreme cold temperatures.

Mesozoic

The geological era that lasted from about 252 to 66 million years ago, including the Triassic, Jurassic, and Cretaceous periods, known for the dominance and eventual extinction of dinosaurs.