Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.



Answer to a math question Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.

Expert avatar
42 Answers
To determine the value of "a" such that the given vectors are coplanar, we can use the fact that three vectors are coplanar if and only if their determinant is equal to zero.

So, let's set up the determinant using the given vectors:

\begin{vmatrix}2 & 2 & -1 \3 & 4 & 2 \a & 2 & 3 \\end{vmatrix}

Expanding the determinant along the top row, we get:

2 \begin{vmatrix}4 & 2 \2 & 3 \\end{vmatrix}- 2 \begin{vmatrix}3 & 2 \a & 3 \\end{vmatrix}- 1 \begin{vmatrix}3 & 4 \a & 2 \\end{vmatrix}

Calculating the determinants:

2((4)(3) - (2)(2))- 2((3)(3) - (2)(a))- 1((3)(2) - (4)(a))


2(12 - 4) - 2(9 - 2a) - 1(6 - 4a)

24 - 8 - 18 + 4a - 6 + 4a

4a + 4a - 8 - 18 - 6

8a - 32

Now, we want the determinant to be equal to zero:

8a - 32 = 0

Solving for "a":

8a = 32

a = \frac{{32}}{{8}} = 4

Answer: The value of "a" that makes the vectors (2,2,−1), (3,4,2), and (a,2,3) coplanar is \boxed{4}.

Frequently asked questions (FAQs)
What is the equation for a hyperbola with center (h,k), horizontal transverse axis, vertex at (h+a,k), and foci at (h±c,k), where a>0 and c>0?
What is the area of a triangle with base 6 cm and height 8 cm?
What is the rule for congruence of triangles when one side and two angles are known?
New questions in Mathematics
-442/c+5=26 what is c?
I need .23 turned into a fraction
The function g:Q→Q is a ring homomorphism such that g(3)=3 and g(5)=5. What are the values of g(8) and g(9)?
2x2 and how much?
A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?
In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left. How many peppers and carrots were there initially?
A test has 5 multiple choice questions. Each question has 4 alternatives, only one of which is correct. A student who did not study for the test randomly chooses one alternative for each question.(a) What is the probability of him getting a zero on the test?(b) What is the probability of him getting a three or more? The maximum mark for the test is 5, with each question worth one point.
User The average height of Aranka, Böske, Cili, Delinke and Lili is 172 cm. We know that Aranka and Cili are both 172 cm tall. The sum of the heights of Böské and Delinke is 336 cm. How tall is Lili?
The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?
In an audience of 4000 people, 2 people are chosen, at random, to appear on stage. How many ways can the people be chosen?
Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0
The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .
If a|-7 and a|9, then a|-63
Express the trigonometric form of the complex z = -1 + i.
How to convert 45 kg into grams
Nancy is a waitress at Seventh Heaven Hamburgers. She wants to estimate the average amount each table leaves for a tip. A random sample of 5 groups was taken and the amount they left for a tip (in dollars) is listed below: $11.00 $8.00 $6.00 $3.00 $7.00 a.) Find a 90% confidence interval for the average amount left by all groups. (*round to the nearest cent*) $ < μ < $ b.) If the sample size were larger, with everything else remaining the same, would the margin of Error increase or decrease? Decrease Increase c.) If the Confidence level were 95% instead of 90%, would the range (size) of the Confidence Interval be larger or smaller? Larger Smaller
7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?
a) 6x − 5 > x + 20
Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.