Calc III

Hello,

Can somebody help me with the following two problems?

1. Find a value of a such that the vector <a, 1,1> makes an angle of 45 degrees with the vector <1,2,1> or show that no such a exists.

---I started by using theta = arccos (u*v)/(absu*absv) must equal (sqrt2)/2 and attempting to solve from there...but I'm not sure if that's the best way to proceed.

2. Let u = 3i + j; v = 5i - 2j; and w = i - j. Find scalars, a and b such that u = av +bw.

I have no idea how to proceed with this one.

I would greatly appreciate any help!!!

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. u = <a, 1,1>

    v = <1,2,1>

    u dot v = 1/2 sqrt(2) |u| |v| ---->

    (u dot v)^2 = 1/2 |u|^2 |v|^2 ---->

    (a+3)^2 = 1/2 (a^2 + 2)*6 ---->

    2 a^2 -6 a -3 = 0

    Let u = 3i + j; v = 5i - 2j; and w = i - j. Find scalars, a and b such that u = av +bw.

    av+bw =

    (5a +b)i + (-2a-b)j

    av+bw = u --->

    5a + b = 3

    2a + b = -1

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. sat essay

    Is it necessary for us to find new solutions to problems? Many people may argue that we don¡¯t need to since we are already able to solve the problems. As far as I am concerned, we should always try to find new solutions to

  2. Algebra 1

    Terry has completed 15 homework problems, and Susan has competed 9. Terry is completing 10 problems per hour and Susan is competing 12 problems per hour. After how many hours will terry and susan have completed the same number of

  3. BUSINESS

    1. You've told Dan, a new contact, that you're looking for a qualified sales representative. Now you want to find out if there's any way you can help his business. What's an effective way to approach the question? A. Give him your

  4. Math-PLEASE check my answers

    What types of problems can be solved using the greatest common factor? What types of problems can be solved using the least common multiple? Complete the explanation. *** Use the words 'same' and 'different' to complete the

  1. Statistics

    Solve the following problems by using the binomial formula. a. If n = 4 and p = .10 , find P(x = 3) . b. If n = 7 and p = .80 , find P(x = 4) . c. If n = 10 and p = .60 , find P(x ¡Ý 7) . d. If n = 12 and p = .45 , find P(5 ¡Ü

  2. Tecnology

    Alex works at his computer for several hours a day. He is careful to sit up straight at the computer with his feet on the floor and to keep his muscles relaxed, and stays off his computer after 6 p.m. For what kind of

  3. Algebra

    Here is the problem: A two-digit number is eight times the sum of its digits.When the number is added to the number obtained by reversing the digits,the sum is 99. Find the original number. Please explain hot to solve it and it

  4. Ed Tech - CHECK MY ANSWERS PLEASE

    I just took an Ed Tech assessment and so could someone check my answers before I turn it in? Thanks!! 1.) What did the STRICT study generally find about the effect of Internet use on sleep? A. Teens who use the Internet and phone

  1. geometry CA

    Graph quadrilateral ABCD. Then determine the most precise name for each quadrilateral. 1. A (0, 5), B (–5, 0), C (0, –5), D (5, 0) (1 point) square kite rectangle 2. A (–4, 4), B (3, 4), C (5, 0), D (–2, 0) (1 point)

  2. math

    You were given 10 math problems for homework. You completed 310 of them at school. Which equation shows how to find the fraction of the problems you still must do to complete your homework?

  3. Math please explain!!

    A student got 80 percent problems correctly which is 32 problems correct. how many problems are they in total? I got 40 in a page but it did not explain can you PLEASE EXPLAIN!!!!

  4. mathematics (Please answer :))

    What is the measure of the smallest angle in the figure? The figure is not drawn to scale. In this problem my test shows a 90 degree angle, and then for the other two angles, there are algebraic problems. Here are the problems. 6x

View more similar questions or ask a new question.