Find the Vector $\mathbf { v }$ That Has a Magnitude of 6 and Is in the Magnitude

question 109

Multiple Choice

Find the vector $\mathbf { v }$ that has a magnitude of 6 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 6 , - 5 \rangle$ .

• A) \(\mathbf { v } = \left\langle \frac { - 36 } { \sqrt { 61 } } , \frac { - 30 } { \sqrt { 61 } } \right\rangle\)
• B) \(\mathbf { v } = \left\langle \frac { - 6 } { \sqrt { 61 } } , \frac { - 5 } { \sqrt { 61 } } \right\rangle\)
• C) \(\mathbf { v } = \left\langle \frac { - 1 } { \sqrt { 61 } } , \frac { - 6 } { \sqrt { 61 } } \right\rangle\)
• D) \(\mathbf { v } = \left\langle \frac { - 1 } { \sqrt { 61 } } , \frac { 1 } { \sqrt { 61 } } \right\rangle\)
• E) \(\quad \mathbf { v } = \left\langle \frac { 5 } { \sqrt { 61 } } , \frac { 6 } { \sqrt { 61 } } \right\rangle\)

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Definitions:

Hyperbola

A type of smooth curve lying in a plane, consisting of two branches, which are mirror images of each other, and asymptotically approaching fixed lines.

Asymptotes

Asymptotes are lines that a graph approaches but never reaches, illustrating behavior towards infinity or certain points within the domain.

Vertices

Vertices are the corner points where two or more lines, edges, or curves meet.

Hyperbola

A type of smooth curve lying in a plane, formed by intersecting a double cone; it has two disconnected branches.