Answer to Question #190167 in Trigonometry for Pete

Question

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)

Answer 1

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

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

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

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

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

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

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

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

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

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

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

$u =\dfrac{i}{\sqrt{2}}+\dfrac{j}{\sqrt{2}}$

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

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

Q1.

1. $║u║ = \sqrt{41}$

2. $║u║ = \sqrt{41}$

3. Yes

Q2.

1. $║u║ =2\sqrt{13}$

2. $║v║= 2√13$

3. Yes

Q3.

1. $║u║ = 6$

2. $║v║= 6$

3. Yes

Q4.

1. $║u║ = 5$

2. $║v║= 5$

3. Yes