A vector A has a magnitude of 5 units and points in the -y direction, while a ve

Question

A vector A has a magnitude of 5 units and points in the -y direction, while a vector B has triple the magnitude of A and points +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 + B magnitude Draw a diagram of the vectors the resultant. What are the components of the vectors? How does scalar multiplication affect the components of a vector? How and do you use components to do vector addition or subtraction? direction Use trigonometric functions to determine the angle. Check this angle against your diagram. Based on the signs of the components, in which quadrant does the vector be? degree (counterclockwise from the +x-axis) A-B unit magnitude direction (counterclockwise from the +x-axis) B - A magnitude direction (counterclockwise from the +x-axis)

Explanation / Answer

A = -5 j

B = (3 x 5) i = 15 i

(A) A + b = 15i - 5j

magnitude = sqrt(15^2 + 5^2) = 15.8 units

Direction = 360 - tan^-1(5/15 ) = 341.6 deg

(B) A - B = -5j - 15i = - 15i - 5j

magnitude = sqrt(15^2 + 5^2) = 15.8 units

direction = 180 + tan^-1(5/15) = 198.4 deg

(C) B - A = 15i - (-5j) = 15i + 5j

magnitude = 15.8 units

DSirection = tan^-1(5/15) = 18.4 deg

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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