1 answer

Show that the line [x,y,z]=[10,5,16]+t[3,1,5] is contained in the plane x+2y-z-4=0 I tries writing the vector equation in parametric form

Question:

Show that the line [x,y,z]=[10,5,16]+t[3,1,5] is contained in the plane x+2y-z-4=0
I tries writing the vector equation in parametric form and then substituting it into the respective x,y,z in the plane, after simplifying I get 0t=0 does this mean that the line is in the plane or did I do something wrong

Answers

Yes, that means that the line is in the given plane.

You can also take any two distinct points on the given line (i.e. two arbitrary values of t) and prove that each of the point lies in the plane..

Similar Solved Questions

1 answer
How do you multiply #(m + 9) ( m ^ { 2} + 3m - 5)#?
How do you multiply #(m + 9) ( m ^ { 2} + 3m - 5)#?...
1 answer
For the following linear system, use Gaussian Eliminations and the concept of rank to determine the...
For the following linear system, use Gaussian Eliminations and the concept of rank to determine the values of a and b for which there are: a. Unique solutions. b. No solutions. c. Infinite solutions. -2x1 + x2 – X3 = 1 3x1 – x2 + 2x3 = 0 -2x1 + x2 + axz = b...
1 answer
Balloons By Sunset (BBS) is considering the purchase of two new hot air baloons so thar...
Balloons By Sunset (BBS) is considering the purchase of two new hot air baloons so thar t can expand its desert sunset tours. Vanous information about the proposed investment follows: Initial investment (or two hot air balloons) 442,000 Sahrage value Annual net income genarated BBSs cost of capial S...
1 answer
Digestive disorders are nothing new. As long as humans have consumed food, there have been problems...
Digestive disorders are nothing new. As long as humans have consumed food, there have been problems with digestion. Now think about how human nutrition has changed over time and across geographical locations. TASK: Identify a digestive disorder that is closely linked to a particular time or place. F...
1 answer
May species can reproduce a오 wolly ad sexuayin host Cohdition be grificone of di's Suithfroim sal...
May species can reproduce a오 wolly ad sexuayin host Cohdition be grificone of di's Suithfroim sal te ses eues rproddion when enywsento cone wifoupcob mfaunrable Sspeculile abuit the evaluih Sigrfeote of ts Swrth frim Gsdal f. se on...
1 answer
Find the component form and magnitude of the vector v. Initial Point Terminal Point (-3,-1) (-11,...
Find the component form and magnitude of the vector v. Initial Point Terminal Point (-3,-1) (-11, 5) V= IV - Need Help? Read It Find the magnitude of the scalar multiple, where u = (2.0) and v = (-3, 6). 1|-2011 11-2v1 = Need Help? Read It Find the vector v with the given magnitude and the same dire...
1 answer
Suppose the synthesis of ethylene dichloride proceeds by the following mechanism: step rate constant elementary reaction...
Suppose the synthesis of ethylene dichloride proceeds by the following mechanism: step rate constant elementary reaction CH,CH, (g)+ci, (g) → CH,CH,ci* (g)+ciº (9) CH,CH,CI* (g)+C1 (g) → CH,CH,C1, (g) Suppose also kq «k2. That is, the first step is much slower than the second. W...
1 answer
#4 Given the Boolean function F(A,B,C) = A'C + A'B + AB'C + BC, a) construct...
#4 Given the Boolean function F(A,B,C) = A'C + A'B + AB'C + BC, a) construct the truth table. b) Simplify the expression and draw the resulting combinational circuit (AND, OR, NOT)....
1 answer
10 and 11, please 10. The fatty acid byproducts of lipid metabolism can be converted to...
10 and 11, please 10. The fatty acid byproducts of lipid metabolism can be converted to acetyl-CoA through a process known as 11. A zone of clearing on a milk agar plate indicates the production of the enzyme (1 point) by the microbe and indicates that the organism has metabolized the protein Lab...
1 answer
1. How much heat is needed to raise the temperature of 3 kg of water from...
1. How much heat is needed to raise the temperature of 3 kg of water from 20oC to 40oC? Give answer in kJ (1kJ = 1000 J) (round answer to 3 sig fig) 2. How much heat is needed to raise the temperature of 3 kg of ice from -40oC to -20oC? (round answer to 3 sig fig) Specific heat of water: C = 4...
1 answer
The problem I'm trying to answer is: Ann is driving down a street at 59 km/h
The problem I'm trying to answer is: Ann is driving down a street at 59 km/h. Suddenly a child runs into the street. If it takes Ann 0.719 s to react and apply the brakes, how far will she have moved before she begins to slow down? Answer in units of m. I know the first step is to convert 59 km...
1 answer
5. You have five different individual aqueous solutions (KCIO2 (aq): LINO, (aq): HNO2 (aq); Lion and...
5. You have five different individual aqueous solutions (KCIO2 (aq): LINO, (aq): HNO2 (aq); Lion and NH4NO3(aq)). These aqueous solutions have different pH values. What is the order of these solutions placed in order of increasing pH: lowest pH to highest pH? A) KClO2 (aq) < NH4NO3(aq) <LINO; ...
1 answer
QUESTION: You are given a meterstick and asked to drill a small hole through it so...
QUESTION: You are given a meterstick and asked to drill a small hole through it so that, when the stick is pivoted about a horizontal axis through the hole, the period of the pendulum will be a minimum. Where should you drill the hole?(give the distance from the end of the meterstick) Hint: The rota...
1 answer
Provide the products of each reaction (3pts, 2pts) 1. HgO* 2. NaOCH3 4. OCH HORD OCH3...
Provide the products of each reaction (3pts, 2pts) 1. HgO* 2. NaOCH3 4. OCH HORD OCH3 3. Η ' Δ 4. NaCN 1. LDA 2. Ph 3. H, A 4. EtMgBr...
1 answer
End A of the 6-kg uniform rod AB of length L = 1.5 m rests on...
End A of the 6-kg uniform rod AB of length L = 1.5 m rests on the inclined surface, while end B is attached to a collar of negligible mass which can slide along the vertical rod shown. When the rod is at rest a vertical force P is applied at B. causing end of the rod to start moving upward with an a...
1 answer
How much HOCl (Ka = 2.5x10-8) (HOCl <=> H+ + OCl- must be added to pure...
How much HOCl (Ka = 2.5x10-8) (HOCl <=> H+ + OCl- must be added to pure water to make a solution of pH 4.3?...
1 answer
Jim Coston was reviewing the latest income statement for Trenton Communications. For the second year in...
Jim Coston was reviewing the latest income statement for Trenton Communications. For the second year in a row, the Audio division was showing a negative segment margin, and Jim thought it was time to close the division to increase the company's operating income. The income statement that he exam...