Finding unit vectors the form an angle with another vector
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Question:
Find two unit vectors in 2-space that make an angle of $45°$ with $4i + 3j$.
I tried letting the other vector, v = ai +bj.
Then I used the dot product trying to obtain and and b,
$(4i+3j).(ai+bj)=5||v||cos45$
$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$
$(16a^2 + 9b^2) = frac{25}{{2}}(a^2+b^2)$
Once I get here, I'm unsure how to progress. I end up with a multi-variable expression I'm not too sure how to solve.
vectors
asked Mar 9 '16 at 10:22
Ron
455
add a comment |
up vote
0
down vote
favorite
Question:
Find two unit vectors in 2-space that make an angle of $45°$ with $4i + 3j$.
I tried letting the other vector, v = ai +bj.
Then I used the dot product trying to obtain and and b,
$(4i+3j).(ai+bj)=5||v||cos45$
$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$
$(16a^2 + 9b^2) = frac{25}{{2}}(a^2+b^2)$
Once I get here, I'm unsure how to progress. I end up with a multi-variable expression I'm not too sure how to solve.
vectors
asked Mar 9 '16 at 10:22
Ron
455
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Question:
Find two unit vectors in 2-space that make an angle of $45°$ with $4i + 3j$.
I tried letting the other vector, v = ai +bj.
Then I used the dot product trying to obtain and and b,
$(4i+3j).(ai+bj)=5||v||cos45$
$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$
$(16a^2 + 9b^2) = frac{25}{{2}}(a^2+b^2)$
Once I get here, I'm unsure how to progress. I end up with a multi-variable expression I'm not too sure how to solve.
vectors
asked Mar 9 '16 at 10:22
Ron
455
Question:
Find two unit vectors in 2-space that make an angle of $45°$ with $4i + 3j$.
I tried letting the other vector, v = ai +bj.
Then I used the dot product trying to obtain and and b,
$(4i+3j).(ai+bj)=5||v||cos45$
$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$
$(16a^2 + 9b^2) = frac{25}{{2}}(a^2+b^2)$
Once I get here, I'm unsure how to progress. I end up with a multi-variable expression I'm not too sure how to solve.
vectors
vectors
asked Mar 9 '16 at 10:22
Ron
455
asked Mar 9 '16 at 10:22
Ron
455
edited Mar 9 '16 at 10:37
asked Mar 9 '16 at 10:22
Ron
455
asked Mar 9 '16 at 10:22
Ron
455
asked Mar 9 '16 at 10:22
Ron
455
455
add a comment |
add a comment |
2 Answers
2
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oldest
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0
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The question asks for two unit vectors, so $|v|=1$.
Also, I don't see a connection between the equation $$(4i+3j).(ai+bj)=5||v||cos45$$
and
$$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$$
Can you explain how one follows from the other? I need to understand your thinking before I can direct it to the answer.
answered Mar 9 '16 at 10:28
5xum
89.1k393160
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
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up vote
0
down vote
Unit vectors have a magnitude of 1, that is why they are called unit. You are looking at two solutions, as the vector you are looking for can be "on both sides" of the given vector.
The system of equations you should be solving is:
4a + 3b = 5/sqrt(2)
a^2 + b^2 = 1
answered Mar 9 '16 at 10:36
Milan C.
112
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The question asks for two unit vectors, so $|v|=1$.
Also, I don't see a connection between the equation $$(4i+3j).(ai+bj)=5||v||cos45$$
and
$$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$$
Can you explain how one follows from the other? I need to understand your thinking before I can direct it to the answer.
answered Mar 9 '16 at 10:28
5xum
89.1k393160
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
add a comment |
up vote
0
down vote
The question asks for two unit vectors, so $|v|=1$.
Also, I don't see a connection between the equation $$(4i+3j).(ai+bj)=5||v||cos45$$
and
$$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$$
Can you explain how one follows from the other? I need to understand your thinking before I can direct it to the answer.
answered Mar 9 '16 at 10:28
5xum
89.1k393160
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
add a comment |
up vote
0
down vote
up vote
0
down vote
The question asks for two unit vectors, so $|v|=1$.
Also, I don't see a connection between the equation $$(4i+3j).(ai+bj)=5||v||cos45$$
and
$$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$$
Can you explain how one follows from the other? I need to understand your thinking before I can direct it to the answer.
answered Mar 9 '16 at 10:28
5xum
89.1k393160
The question asks for two unit vectors, so $|v|=1$.
Also, I don't see a connection between the equation $$(4i+3j).(ai+bj)=5||v||cos45$$
and
$$(4a + 3b) = frac{5}{sqrt{2}}||v||sqrt{a^2+b^2}$$
Can you explain how one follows from the other? I need to understand your thinking before I can direct it to the answer.
answered Mar 9 '16 at 10:28
5xum
89.1k393160
answered Mar 9 '16 at 10:28
5xum
89.1k393160
answered Mar 9 '16 at 10:28
5xum
89.1k393160
answered Mar 9 '16 at 10:28
5xum
89.1k393160
89.1k393160
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
add a comment |
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
I edited my question, I had one too many ||v||'s!
– Ron
Mar 9 '16 at 10:38
add a comment |
up vote
0
down vote
Unit vectors have a magnitude of 1, that is why they are called unit. You are looking at two solutions, as the vector you are looking for can be "on both sides" of the given vector.
The system of equations you should be solving is:
4a + 3b = 5/sqrt(2)
a^2 + b^2 = 1
answered Mar 9 '16 at 10:36
Milan C.
112
add a comment |
up vote
0
down vote
Unit vectors have a magnitude of 1, that is why they are called unit. You are looking at two solutions, as the vector you are looking for can be "on both sides" of the given vector.
The system of equations you should be solving is:
4a + 3b = 5/sqrt(2)
a^2 + b^2 = 1
answered Mar 9 '16 at 10:36
Milan C.
112
add a comment |
up vote
0
down vote
up vote
0
down vote
Unit vectors have a magnitude of 1, that is why they are called unit. You are looking at two solutions, as the vector you are looking for can be "on both sides" of the given vector.
The system of equations you should be solving is:
4a + 3b = 5/sqrt(2)
a^2 + b^2 = 1
answered Mar 9 '16 at 10:36
Milan C.
112
Unit vectors have a magnitude of 1, that is why they are called unit. You are looking at two solutions, as the vector you are looking for can be "on both sides" of the given vector.
The system of equations you should be solving is:
4a + 3b = 5/sqrt(2)
a^2 + b^2 = 1
answered Mar 9 '16 at 10:36
Milan C.
112
answered Mar 9 '16 at 10:36
Milan C.
112
answered Mar 9 '16 at 10:36
Milan C.
112
answered Mar 9 '16 at 10:36
Milan C.
112
112
add a comment |
add a comment |
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