Question #190167

Can anyone help with this trig HW?


In Exercises 39-46, find the unit vector that has the same direction as the unit vector v.

39. V= 6i

40. v = 5j

41. v=3i-4j

42. v= 8i-6j

43. v = 3i -2j

44. v = 4i-2j

45. v = i + j

46. v = i - j


Are the Vectors Equal?

1. Find ║u║ 

2. Find ║v║

3. Is u = v?

Explain

Q1. The points on u are (-1,2) and (4,6)

The points on v are (0,0) and (5,4)


Q2. The points on u are (-4,6) and (0,0)

The points on v are (-2,5) and (2,-1)


Q3. The points on u are (-1,1) and (5,1) 

The points on v are (-2,-1) and (4,-1)


Q4. The points on u are (-3,3)and (-3,-2) 

The points on v are (3,1) and (3,-4)


1
Expert's answer
2021-05-17T03:50:03-0400

1. V=6iV=62=6u=6i/6=i1.\ V = 6i\\ |V| = \sqrt{6²} = 6\\ u = 6i/6 = i


2. V=5jV=52=5u=5j/5=j2.\ V= 5j\\ |V| = \sqrt{5²} = 5 \\ u = 5j/5 = j


3. V=3i4jV=32+42=53.\ V = 3i-4j\\ |V| = \sqrt{3²+4²} = 5


u=3i4j5=3i54j5u = \dfrac{3i-4j}{5} = \dfrac{3i}{5} -\dfrac{4j}{5}


4. V=8i6jV=82+62=104. \ V = 8i-6j\\ |V| = \sqrt{8²+6²} = 10


u=8i6j5=4i53j5u = \dfrac{8i-6j}{5} = \dfrac{4i}{5} -\dfrac{3j}{5}


5. V=3i2jV=32+22=135.\ V = 3i-2j\\ |V| = \sqrt{3²+2²} = \sqrt{13}


u=3i132j13u = \dfrac{3i}{\sqrt{13}}- \dfrac{2j}{\sqrt{13}}


6. V=4i2jV=42+22=256.\ V = 4i-2j\\ |V| = \sqrt{4²+2²} = 2\sqrt5


u=2i5j5u =\dfrac{2i}{√5} -\dfrac{j}{\sqrt{5}}


7. V=i+jV=12+12=27.\ V = i+j\\ |V| = \sqrt{1²+1²} = \sqrt2


u=i2+j2u =\dfrac{i}{\sqrt{2}}+\dfrac{j}{\sqrt{2}}


8. V=ijV=12+12=28.\ V = i-j\\ |V| = \sqrt{1²+1²} = \sqrt2


u=i2j2u =\dfrac{i}{\sqrt{2}} -\dfrac{j}{\sqrt{2}}


Q1.

1. u=41║u║ = \sqrt{41}

2. u=41║u║ = \sqrt{41}

3. Yes


Q2.

1. u=213║u║ =2\sqrt{13}

2. v=213║v║= 2√13

3. Yes


Q3.

1. u=6║u║ = 6

2. v=6║v║= 6

3. Yes


Q4.

1. u=5║u║ = 5

2. v=5║v║= 5

3. Yes


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