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
Ksju [112]
3 years ago
6

in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
4 0

Answer:

The component of \vec u orthogonal to \vec a is \vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right).

Step-by-step explanation:

Let \vec u and \vec a, from Linear Algebra we get that component of \vec u parallel to \vec a by using this formula:

\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a (Eq. 1)

Where \|\vec a\| is the norm of \vec a, which is equal to \|\vec a\| = \sqrt{\vec a\bullet \vec a}. (Eq. 2)

If we know that \vec u =(2,1,1,2) and \vec a=(4,-4,2,-2), then we get that vector component of \vec u parallel to \vec a is:

\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)

\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)

\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)

Lastly, we find the vector component of \vec u orthogonal to \vec a by applying this vector sum identity:

\vec  u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a} (Eq. 3)

If we get that \vec u =(2,1,1,2) and \vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right), the vector component of \vec u is:

\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10}    \right)

\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)

The component of \vec u orthogonal to \vec a is \vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right).

You might be interested in
I need some help with math
Valentin [98]

Answer:

PT, VP

Step-by-step explanation:

if p is the center and T V and W are on the circle

the radius goes from the center of the circle to the edge of the circle

then PW PT and PW are radii of the circle


6 0
3 years ago
An acre of land planted with sugar beet produces 550 gallons of ethanol from the sugar by fermentation. A car converted to run o
valkas [14]

Answer:

Step-by-step explanation:

a

fdsa

4 0
3 years ago
Find the measure of CP
dmitriy555 [2]

Given:

A figure ABCP.

To find:

The measure of CP.

Solution:

In triangles ABP and CBP,

\angle PAB\cong \angle PCB            (Given right angles)

\angle ABP\cong \angle CBP            (Given)

BP=BP            (Common side)

Now,

\Delta ABP\cong \Delta CBP        (By AAS property of congruence)

We know that the corresponding parts of congruent triangles are congruent.

AP=CP

8=CP

Therefore, the measure of CP is 8 units.

6 0
3 years ago
Can someone help with this question please?
Ilia_Sergeevich [38]

Answer:

D. x = 5

Step-by-step explanation:

I graped the equation on the graph below.

If this answer is correct, please make me Brainliest!

5 0
3 years ago
Answer A , B , C or D. Need some help!
creativ13 [48]

Answer:

c

Step-by-step explanation:

system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. ... The solution to the system will be in the point where the two lines intersect.

3 0
3 years ago
Other questions:
  • A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. A and C are points on the
    7·1 answer
  • What’s the answer to this problem???
    15·1 answer
  • What is the prime factorization of 50 using exponents
    5·1 answer
  • Solve using standard algorithm 57.03+2.08
    15·1 answer
  • Ms. Weaver plans to decorate the bulletin board in her classroom. She purchased 30 sheets of construction paper for $0.30 per sh
    13·1 answer
  • PLS HELP ME !!!!<br> The last one is (x+2)^2 + (y-1) ^2 = 12
    14·1 answer
  • The points L, M, N and O all lie on the same line segment, in that
    11·1 answer
  • Kate lanes a letter against her house to get to the roof. The house is 25 feet tall and I put a ladder is 15 feet away from the
    9·1 answer
  • A dilation has center (0,0). Find the image of the point B ( 5/3, -7/2) for the scale factor 1/3​
    12·1 answer
  • The cube root of the difference of a number and 2
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!