For the following questions, say you were given a line and a plane as below ...

For the following questions, say you were given a line and a plane as below

Line: r(t)= < x(t), y(t), z(t) > = < t-2, t+1, 3t > , Plane: : a(x+2) + b(y-3) - 4z = 2

a) What relationship would have to exist between scalars a and b for the line not to intersect with the plane?

Hint 1) Plug in x, y, z given in the line into the plane equation.

Hint 2) Say you were solving this equation and got the following. What would that indicate?

i) t = 2: ________________________________________________________

ii) 6 = –5: ________________________________________________________

iii) 4 = 4: ________________________________________________________

So what must be true about the coefficient of t? What also can’t be true about the constant term?

b) What relationship would have to exist between scalars a and b for the plane to contain the line?

c) Assuming the line is not contained in the plane but does intersect it, give an expression for the time t that the line intersects the plane. Also give the point of intersection.
(Both answers will have scalars a and b in them)

Expert Solution

Colby Messinger answered 6 months ago

Recall that given a line L1 in the plane with slope m, a second line L2...

Recall that given a line L1 in the plane with slope m, a second line L2 is perpendicular to L1 if and only if the slope of L2 is − 1 m . Now consider the function h(x) = x^2 + 3/2x + 3. Among all of the lines tangent to the graph of h(x), there is exactly one which is perpendicular to the line given by y = −2x + 7. Write the equation of that line tangent to...

) Given the true statements as below, answer the following questions: (a) If Joe is not...

) Given the true statements as below, answer the following questions: (a) If Joe is not a French major and he is not happy, then he doesn’t like to travel. (b) The statement “If Joe knows Discrete Math or he is a CS major, then he is either happy or a CS major.” is false . (c) If Joe is a Math major, then he does not know Discrete Math. (d) If Joe is not a CS major, then he...

Use the following information to answer the questions below. The balances listed below were taken from...

Use the following information to answer the questions below. The balances listed below were taken from the ABC Inc.’s unadjusted trial balance on January 31st. The company’s reporting period began on January 1st . Accounts Receivable $23,000 Accumulated Depreciation 27,000 Accounts Payable 40,000 Cash 22,000 Common Stock 50,000 Equipment 72,000 Land 2,000 Long-term investment 55,000 Prepaid Rent 18,000 Retained Earnings (Beginning) 56,000 Salaries Expense 15,200 Service Revenue 42,200 Supplies 5,000 Utilities Expense 3,000 In addition, assume the following: A. There...

Let’s say you push the block from the bottom of the plane all the way up...

Let’s say you push the block from the bottom of the plane all the way up to the top of the plane, then let it slide back down. 11-1. While you are pushing the block up the plane, is the work done by gravity positive or negative? Why? 11-2. While you are pushing the block up the plane, is the work done by friction positive or negative? Why? 11-3. As the block slides back down the plane, is the work...

Find the equations of the line in the half-plane model of the hyperbolic plane that passes...

Find the equations of the line in the half-plane model of the hyperbolic plane that passes through the points (a) (1,1) and (1,6). (b) (2, 2) and (4,4)

Marketing Scenario B: You are a supplier of a product line. Given the information below, answer...

Marketing Scenario B: You are a supplier of a product line. Given the information below, answer each of the questions asked. You are given the following information (2017 Annual): Price per Unit $25.00 Advertising $15,000 Packaging per unit $ 5.00 Direct Labor per unit $ 8.00 Depreciation $25,000 Royalties per unit $ 2.00 Plant and Equipment $50,000 Total Units Sold 10,000 Your firm’s Total Assets are $400,000 with total equity of $75,000. Using the Contribution Margin PRICE PER UNIT METHOD,...

I. Given the following code segment below what is the best description of line 5 and...

I. Given the following code segment below what is the best description of line 5 and line 6? Identify the public and private members. 1. #include <iostream.h> 2. class SimpleCat 3. { 4. public: 5. SimpleCat (int age, int weight); 6. ~SimpleCat(){} 7. int GetAge() {return itsAge;} 8. int GetWeight() {return itsWeight;} 9. private: 10. int itsAge; 11. int itsWeight; 12. }; II. Multiple Choice questions 1. A function that is called automatically each time an object is created or...

If you were an investment planner how would you address these questions below. What would you...

If you were an investment planner how would you address these questions below. What would you conclude about your personal investment preferences, and how would you support a client who shares your personal investment preferences? What do you expect to happen to attitudes on risk as you age?

Characteristic Line and Security Market Line You are given the following set of data: HISTORICAL RATES...

Characteristic Line and Security Market Line You are given the following set of data: HISTORICAL RATES OF RETURN Year NYSE Stock X 1 - 26.5% - 17.0% 2 37.2 16.0 3 23.8 14.0 4 - 7.2 5.0 5 6.6 9.9 6 20.5 19.4 7 30.6 17.9 Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X's beta coefficient. Round your answer to two decimal places. Beta = Determine the arithmetic average rates of return for...

[The following information applies to the questions displayed below.] The following account balances were selected from...

[The following information applies to the questions displayed below.] The following account balances were selected from the records of TAC Corporation at the end of the fiscal year after all adjusting entries were completed: Common stock ($17 par value; 104,000 shares authorized, 43,000 shares issued, 38,000 shares outstanding) $ 731,000 Additional paid-in capital 169,000 Dividends declared and paid during the year 12,000 Retained earnings at the beginning of the year 75,000 Treasury stock at cost (5,000 shares) (40,000 ) Net...

Question