Review help, again.

Suppose the angle (theta) between vectors u and v is 30, u = (5,4) and llvll = 6.
a. How many possibilities are there for v?
b. Sketch a diagram that shows u and v as position vectors.
c. Find horiztonal and vertical components for a vector v that satisfies the above criteria.

Consider a triangle with standard labeling in which alpha = 3pie/5 rad., b = 7 and a = 12
a. Is it uniquely determined? Justify your response.
b. Solve the triangle.

Bill is 10 miles due north of Ron. Sue is 15 miles away from Ron and 7 miles away from Bill, in the north east. What bearing should Ron take to reach Sue?

Thanks for all the help in advanced. (A quick note, please don't just provide me for answers. I'd appreciate details of how you got your answer and why.)

Quote:

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Originally Posted by SimonYeahh

Suppose the angle (theta) between vectors u and v is 30, u = (5,4) and v = 6.← What does that mean?
a. How many possibilities are there for v?
b. Sketch a diagram that shows u and v as position vectors.
c. Find horiztonal and vertical components for a vector v that satisfies the above criteria.

Consider a triangle with standard labeling in which alpha = 3pie/5 rad., 5 = 7 and a = 12 ← What does that mean?
a. Is it uniquely determined? Justify your response.
b. Solve the triangle.

Bill is 10 miles due north of Ron. Sue is 15 miles away from Ron and 7 miles away from Bill, in the north east. What bearing should Ron take to reach Sue?

Thanks for all the help in advanced. (A quick note, please don't just provide me for answers. I'd appreciate details of how you got your answer and why.)

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Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

Thanks for replying Subhotosh Khan, I don't know where to start. Perhaps some guidance or hints on how to start would be nice. Thank you kindly. I almost re edit the post the make some corrections.

Quote:

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Originally Posted by SimonYeahh

Suppose the angle (theta) between vectors u and v is 30, u = (5,4) and llvll = 6.
a. How many possibilities are there for v?
b. Sketch a diagram that shows u and v as position vectors.
c. Find horiztonal and vertical components for a vector v that satisfies the above criteria.

Consider a triangle with standard labeling in which alpha = 3pie/5 rad., b = 7 and a = 12
a. Is it uniquely determined? Justify your response.
b. Solve the triangle.

Bill is 10 miles due north of Ron. Sue is 15 miles away from Ron and 7 miles away from Bill, in the north east. What bearing should Ron take to reach Sue?

Thanks for all the help in advanced. (A quick note, please don't just provide me for answers. I'd appreciate details of how you got your answer and why.)

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1. It depends how you define an angle, but the first step should be: Draw a sketch.

2. The dotted circle-line belongs to a circle with r = 6. That's the length of [TEX]\vec v[/TEX].

3. The red vectors form an angle with [TEX]\vec u[/TEX] using the tail of [TEX]\vec u[/TEX] as vertex.

4. The green vectors form an angle with [TEX]\vec u[/TEX] using the head of [TEX]\vec u[/TEX] as vertex.

Quote:

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Originally Posted by SimonYeahh

Bill is 10 miles due north of Ron. Sue is 15 miles away from Ron and 7 miles away from Bill, in the north east. What bearing should Ron take to reach Sue?

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Do you not recognize that as a 7-10-15 triangle?
Use Law of Cosines.

Quote:

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Originally Posted by SimonYeahh

Suppose the angle (theta) between vectors u and v is 30, u = (5,4) and llvll = 6.
a. How many possibilities are there for v?
b. Sketch a diagram that shows u and v as position vectors.
c. Find horiztonal and vertical components for a vector v that satisfies the above criteria.

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Let [TEX]v=<a,b>[/TEX].
You know that if [TEX]\theta [/TEX] is the angle between [TEX]u~\&~v[/TEX] then
[TEX]\cos(\theta)=\dfrac{u\cdot v}{\|u\|~\|v\|}[/TEX].

Now you have all that is needed to find [TEX]a~\&~b.[/TEX]