Vector Kinematics
A two-dimensional vector's initial point is \((3,-2)\) and the vector has a magnitude of \(12.\) This vector forms a \(45^{\circ}\) angle with the \(+x\) direction. What is the terminal point of the vector?
A woman moves \(4\text{ m}\) east, \(1\text{ m}\) south, and \(4\text{ m}\) west. What is the direction of the displacement vector of the woman?
An object on a tabletop moves in a straight line, in a direction that forms a \(60^{\circ}\) angle with a ruler. The position of the object read from the ruler was \(10\text{ cm}\) when it started moving. The object then stops when its position read from the ruler is \(32\text{ cm}.\) What is the displacement of the object?
A vector's initial point is \((4,8)\) and terminal point is \((16,-8)\) on the coordinate plane. Find the magnitude of the vector.
Tom walked \(21\text{ miles}\) north, and then \(28\text{ miles}\) east. How far is he from his original location?