2. -/6 pointsWAColPhysAV1 3.P.009 A vector A has a magnitude of 8 units and poin

Question

2. -/6 pointsWAColPhysAV1 3.P.009 A vector A has a magnitude of 8 units and points in the -y-direction, while a vector B has half the magnitude of A and points in the +x-direction. What are the magnitude and direction of the following vectors? Give the directions of each as an angle measured counterclockwise from the +x-direction. (a) A B magnitude direction unit(s) o (counterclockwise from the +x-axis) (b) A - EB magnitude direction unit(s) o (counterclockwise from the +x-axis) (c) B A magnitude direction unit(s) o (counterclockwise from the +x-axis)

Explanation / Answer

a)

we have:

A = -8j

B = 4i

R = A + B

R = (-8j) + (4i)

= (Ax + Bx)i + (Ay + By)j

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

= 4i- 8j

magnitude of R = sqrt (4^2 + -8^2)

magnitude of R = 8.94 units

Since x component is positive and y component is negative

It lies in the 4th cordinate

angle = 270 + atan(|x/y|)

angle = 270 + atan(|4/-8|)

angle = 297 degree

Answer:

8.94 units

297 degree

b)

we have:

A = -8j

B = 4i

R = A - B

R = (-8j) - (4i)

= (Ax - Bx)i + (Ay - By)j

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

= -4i- 8j

magnitude of R = sqrt (-4^2 + -8^2)

magnitude of R = 8.94 units

Since x component is negative and y component is also negative

It lies in the 3rd cordinate

angle = 180 + atan(|y/x|)

angle = 180 + atan(|-8/-4|)

angle = 207 degree

Answer:

8.94 units

207 degree

C)

R = B - A

R = (4i) - (-8j)

= (Bx - Ax)i + (By - Ay)j

= (4 )i + (0 + 8)j

= 4i+ 8j

magnitude of R = sqrt (4^2 + 8^2)

magnitude of R = 8.94 units

Since x component is positive and y component is also positive

It lies in the 1st cordinate

angle = atan(y/x)

angle = atan(8/4)

angle = 63.4 degree

Answer:

8.94 units

63.4 degree

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.