Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Answers

Answer 1

Answer: The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)*(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\n1&1&1\n4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$(\mathbf v)/(\|\mathbf v\|)=(\vec i+3\,\vec j-4\,\vec k)/(√(1^2+3^2+(-4)^2))=\frac1{√(26)}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .

Related Questions

3) g(x) = 4xh(x) = -3x^2 + 4Find (g + h)(x)
The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. make a system of equations to find the smallest number of busses the orchestra can rent. Let x= the number of busses and y= the number of vans make an equation representing the number of vehicles needed. __________ make an equation representing the total number of seats in vehicles for the orchestra members. __________ Solve the system of equations. How many busses does the orchestra need to rent? ____________ How many 12-passenger vans does the orchestra need to rent? ____________
URGENT!! NEED HELP!! SOLVE FOR THE COS(
Write an expression for "777 divided by ccc."
The ratio of the measure of the angels of a triangle is 6:10:2 find the measure of the smallest angle

Find the slope of the line that contains the following points ( -3 , 7) and (8, -2)

Answers

Answer:

-9/11

Step-by-step explanation:

The slope of a line given two points is

m = (y2-y1)/(x2-x1)

= (-2-7)/(8--3)

= (-9)/(8+3)

=-9/11

Hope this helped you. :)

Find the prime factorization of
72

Answers

Answer:

72 = {2,2,2,3,3}

Step-by-step explanation:

2433

Suppose a professor splits their class into two groups: students whose last names begin with A-K and students whose last names begin with L-Z. If p1 and p2 represent the proportion of students who have an iPhone by last name, would you be surprised if p1 did not exactly equal p2? If we conclude that the first initial of a student's last name is NOT related to whether the person owns an iPhone, what assumption are we making about the relationship between these two variables?

Answers

a) Even if the distribution of iPhones by last name is completely uniform in the population generally, there is no reason to believe that the proportions in the sample represented by the class will be identical.
I would not be surprised to see p1 ≠ p2.

b) Saying the variables are not related is the same as saying the variables are independent.

S varies inversely as G. If S is 8 when G is 1.5, find S when G is 3. a) Write the variation. b) Find S when G is 3.

Answers

Step-by-step explanation:

$s \: = (k)/(g)$

$8 = (k)/(1.5)$

$k \: = 1.5 * 8 = 12$

$s = (12)/(g)$

$s = (12)/(3)$

s = 4

A physical education class has 21 boys and 9 girls. Each day, the teacher randomly selects a team captain. Assume that no student is absent. What is the probability that the team captain is a girl two days in a row?The probability of choosing a captain that is a girl two days in a row is
9
%.

Answers

The probability of choosing a captain that is a girl two days in a row is 9%

How to determine the probability?

The given parameters are:

Boys = 21

Girls = 9

The total number of students is

Total = 21 + 9

Total = 30

This means that the probability of selecting a girl is:

P(Girl) = 9/30

For two days, the required probability is

P = 9/30 * 9/30

Evaluate

P = 9%

Hence, the probability of choosing a captain that is a girl two days in a row is 9%

Answers

Answer:

a. If the distribution was normal, many values would be negative, what is incompatible with the response variable (hours dedicated to volunteer activities).

b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.

c. The 95% confidence interval for the mean is (13.307, 16.213).

Step-by-step explanation:

a. If the distribution was normal, the values with one or more standard deviation below the mean would be negative, what is incoherent for this case. This, in a normal distribution, represents approximately 16% of the values.

If we calculate the probabilty for a normal distribution with the sample parameters, the probability of having "negative hours" is 18.6% (see picture attached).

b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.

The sampling distribution standard deviation is also reduced by a factor of 1/√n.

c. We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=14.76.

The sample size is N=500.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=(s)/(√(N))=(16.54)/(√(500))=(16.54)/(22.3607)=0.7397$