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denis23 [38]
3 years ago
15

Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fraction

s where needed.)
Mathematics
1 answer:
joja [24]3 years ago
7 0

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

a = 2i + j -3k

b = 3i - 2j -k

Required

The angle between them

The cosine of the angle between them is:

\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}

First, calculate a.b

a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)

Multiply the coefficients of like terms

a \cdot b =2 * 3 - 1 * 2 - 3 * -1

a \cdot b =7

Next, calculate |a| and |b|

|a| = \sqrt{2^2 + 1^2 + (-3)^2

|a| = \sqrt{14

|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}

|b| = \sqrt{14}

Recall that:

\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}

This gives:

\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}

\cos(\theta) = \frac{7}{14}

\cos(\theta) = 0.5

Take arccos of both sides

\theta =\cos^{-1}(0.5)

\theta =60^o

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Kayla wants to find the width, AB, of a river. She walks along the edge of the river 65 ft and marks point C. Then she walks 25
AlladinOne [14]

Answer:

Part A) The triangles ABC and EDC are similar by AAA, because the three internal angles are equal in both triangles

Part B) The width of the river is about 39\ ft

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

Part A) we know that

In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent

so

m<DCE=m<ACB -----> by vertical angles  

m<EDC=m<ABC -----> is a right angle

m<DEC=m<CAB -----> the sum of the internal angles must be equal to 180 degrees

Part B) we know that

The triangles ABC and EDC are similar -------> see Part A

therefore

\frac{BC}{DC}=\frac{AB}{DE}

substitute the values and solve for AB

\frac{65}{25}=\frac{AB}{15}

AB=15*(\frac{65}{25})=39\ ft

8 0
3 years ago
Need help with this one also
-Dominant- [34]

Answer:

D

Step-by-step explanation:

10/7 = 1.4285

9/y = 1.4285

Multiply both sides by y.

9 = 1.4285y

Divide both sides by y.

6.3 = y

6 0
2 years ago
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Answer: 3.75

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

W (3 , y), origin (0 ,0)

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Step-by-step explanation:

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