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? asked in Science & MathematicsMathematics · 2 years ago

Calculus questions?

1. Show and/or explain that u = v.

2. Find the component form AND the magnitude of the vector v with initial point (1, 11) and terminal point (9, 3).

3. Write your answer as a vector in the form <a, b>.

A. Let u = <7, -3> and v = <-2, 4>. Find 3v.

B. Let u = <7, -3> and v = <-2, 4>. Find -8u.

C. Let u = <7, -3> and v = <-2, 4>. Find u + 3v.

D. Let u = <7, -3> and v = <-2, 4>. Find u - v.

4. Find the direction angle for vector v. If necessary, round your answer to the nearest tenth of a degree.

A. v = 8i - 10j

B. w = -4i - 3j

Attachment image

2 Answers

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  • 2 years ago

    (1)

    u=(0-(-3))i+(4-(-4))j=3i+8j

    v=(3-0)i+(3-(-5))j=3i+8j

    =>

    u=v

    (2)

    v=? Do it yourself with reference

    to (1)

    (3) v=<2,4>; u=<7,-3>

    =>

    A) 3v=3<2,4>=<6,12>

    B) -8u=(-8)<7,-3>=<-56,24>

    C) u+3v=<7,-3>+<6,12>=<13,9>

    D) u-v=<7,-3>-<2,4>=<5,-7>

    (4)

    A) v=8i-10j=>

    angle=tan^-1(-10/8)=308.7*

    B) w=-4i-3j=>

    angle=tan^-1(-3/(-4))=216.9*

    approximately.

    (Measured counterclockwise).

    or

    A) angle=-51.3* approximately

    (Measured clockwise).

  • 2 years ago

    #1. Both u and v are -3i - 8j, or <-3, -8>.

    #2. Component form is 8i - 8j, or <8, -8>.

    Magnitude is 8*sqrt(2).

    #3. (A) 3v = <-6, 12>. (B) -8u = <-56, 24>.

    (C) u + 3v = <1, 9>. (D) u - v = <9, -7>.

    #4. (A) arctan(-10/8) = about 310 degrees but use a calculator.

    (B) arctan(-3/-4) = about 215 degrees but use a calculator.

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