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
Zina [86]
3 years ago
14

Find a unit vector that has the same direction as the given vector. 8i ? j + 4k

Mathematics
1 answer:
e-lub [12.9K]3 years ago
7 0

Answer with Step-by-step explanation:

a.Let given vector

a=8i-j+4k

\mid a\mid=\sqrt{(8)^2+(-1)^2+(4)^2}=9

By using the formula

Magnitude of a vector=\sqrt{x^2+y^2+z^2}

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector=\hat{a}=\frac{a}{\mid a\mid}

By using the formula

The unit vector=\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k

b.Let vector b=-2i+4j+2k

\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6

\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by =6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}

The vector in the direction of <-2,4,2> with length 6 is given by =-\sqrt 6(-i+2j+k)

c.\theta=\frac{\pi}{3}

\mid v\mid=8

Let v=v_x i+v_y j

v_x=\mid v\mid cos\theta

v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4

cos\frac{\pi}{3}=\frac{1}{2}

v_y=\mid v\mid sin\theta

v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3

sin\frac{\pi}{3}=\frac{\sqrt 3}{2}

Therefore, the vector v in component form=4i+4\sqrt 3j

You might be interested in
A chef bought 0.69 kilograms of almonds and 0.64 kilograms of pecans. How many
stellarik [79]

Answer: 1.33 kg

Step-by-step explanation:

8 0
3 years ago
What is 45% of $360
Elis [28]
45 percent of 360 is 162.
3 0
3 years ago
Read 2 more answers
What is y? <br><br> Enter your answer in the box
Bogdan [553]
The answer is 97, because when you add up 42 and 55 you get 97. Then you subtract that by 180 because a triangles angles add up to 180. 180-97=83. Z=83. Z and y are supplementary to eachother, so therefore 180-83= 97. Supplementary means they add up to 180.
5 0
3 years ago
Suppose the heights of adult men are normally distributed. The heights of a sample of 30 men are shown below, in inches. 65, 83,
sweet [91]

Answer: Mean-70. Standard Deviation-5.228

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
ANSWER NOWWW PLEASEEEEWhat operation is represented in the expression 4 (2+4)?
user100 [1]
Product difference would be it
8 0
3 years ago
Other questions:
  • Mischa wrote, “Anderson has ten trading cards. He gives some to Desai.” This describes a possible context for the expression x m
    5·2 answers
  • A sales clerk's daily earnings include $125 per day plus commission equal to x percent of his daily sales.
    5·1 answer
  • Simplify the given expression:
    15·1 answer
  • Carla had $40 to spend at the mall. she spent 20% of her money on lunch and 3/4 of her remaining money on a necklace. what fract
    12·1 answer
  • What is the total surace area of the cylinder? Write your answer as a polynomial in standard form.
    6·2 answers
  • What is 9(3x+5+x) solve without using parentheses
    11·1 answer
  • A new computer system sells for approximately $2000 and depreciates at the rate of $500 per year.
    6·1 answer
  • What is the slope of a line perpendicular to a line that's passes through (3,8) and (1,-4)?
    11·1 answer
  • The sum of - 6a and 7a is - 31
    8·1 answer
  • Brainliest to correct answer first!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!