9514 1404 393
Answer:
- u, AB
- 6.4
- arctangent
- 51°
- MN has the opposite direction of NM
- a ray has infinite length; a vector has finite length
Step-by-step explanation:
1. The problem preamble gives you the two ways to name the vector. You can use either its name, or the two end points. (The starting point is named first, as it is with a ray.)
The vector shown can be referred to by the names ...
u or AB
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2. The right triangle has legs 4 and 5, so the length is ...
length = √(4² +5²) = √41
length ≈ 6.4
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3. Typically, you're given the leg lengths. The ratio of these is the tangent of the angle. The angle can be found using the inverse tangent function.
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4. The tangent of the angle is the slope of the vector:
tan(A) = 5/4
A = arctan(5/4) ≈ 51°
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5. The first letter named is the starting point of the vector. Vector MN starts at point M and ends at point N. Vector NM starts at N and ends at M. The directions of the two vectors are opposites.
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6. A ray is like a vector of infinite length. The name of a ray includes a point on the ray. The name of a vector includes both end points. It is of finite length.
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<em>Additional comment</em>
A lot of math is invented to describe how things work in the real world. A vector is often used to represent velocity or force and other things that can be described by a magnitude and direction in the real world. A ray is more often used in problems in geometry, where that abstract concept serves a useful purpose.
