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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
2 Answers
- PinkgreenLv 72 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).
- az_lenderLv 72 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.