1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inysia [295]
2 years ago
5

Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B

A and BC is equal to 4. Round your answer to 2 decimal places.
Mathematics
1 answer:
Vilka [71]2 years ago
3 0

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

You might be interested in
-2(0)^2-3(0)+8 solve for math
Ksivusya [100]
If we times 0 with any number, we can get 0. Then only 8 will remain
8 is the answer.
8 0
3 years ago
You could win a giant jar of jelly beans if only you could guess how many are in the jar. You find a smaller jar such that the g
Gennadij [26K]

The giant jar of jelly beans is 5 times the size of the smaller jar. If there are 83 jelly beans in the smaller jar, the giant jar can be represented as 5(83).

5(83) = 415 jelly beans

4 0
3 years ago
Read 2 more answers
If the rejection region is +1.10, what will be your decision if the z computed value is 2.34
IRINA_888 [86]

The decision when the z value is within the rejection region is that we'll have to reject the null hypothesis.

<h3>What is a rejection region?</h3>

It should be noted that the rejection region is also known as the critical region. It is the set of values where the null hypothesis is rejected.

When the observed test statistic is in the rejection region, we'll have to reject the null hypothesis and then accept rte alternative hypothesis.

Learn more about z scores on:

brainly.com/question/6096474

#SPJ1

7 0
2 years ago
TRAY A tray in a school cafeteria has the dimensions shown. Find the area of the tray.
babymother [125]

Answer:

This is your answer

4 0
3 years ago
Use the order of operations to simplify the expression. PLEASE EXPLAIN
lilavasa [31]
Its 23, you do the times first then add.
3x5=15
15+8=23
6 0
3 years ago
Other questions:
  • What are the common mutiples of 3 and 12
    13·2 answers
  • Exponential Functions
    10·1 answer
  • Is a rectangle a quadrilateral
    9·2 answers
  • What is the definition of a line​
    8·2 answers
  • The equation y = ax describes the graph of a line. If the value of a is positive, the line:
    11·2 answers
  • What is five million four thousand three hundred in standard form
    8·2 answers
  • Y = f(x) = 2x<br> Find f(x) when x = 2.<br> Enter the correct answer.
    6·2 answers
  • Does anyone know how to solve this problem
    9·1 answer
  • If 18 plums weigh 54 ounces, then 6 plums weigh how many<br> ounces?
    10·2 answers
  • What is the classification of the pair of angles shown?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!