Exam 38:Vectors in the Plane

If $\| \mathbf { u } \| = 4$ and $\| \mathbf { v } \| = 6$ ,and the vectors make angles of 140° and 20° with the x-axis respectively,find the component form of the sum of u and v.Round answers to two decimal places.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9,9)​ ​(10,-10)

?Find the vector v that has a magnitude of 9 and is in the same direction as u,where $\mathbf { u } = \langle 6 , - 5 \rangle$ . ?

Find the magnitude and direction angle of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$ .

Find u + v.? $\mathbf { u } = \langle 4,5 \rangle , \mathbf { v } = \langle 6,0 \rangle$ ?

Using the figure below,sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.]? $-u$ ?

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place. ​

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. ​​ ​ Where b = 28° ​

Find the component form of v if $\| \mathbf { v } \| = 6$ and the angle it makes with the x-axis is 150°.

Given that Force 1 = 55 pounds and Force 2 = 130 pounds,find the angle between the forces if the magnitude of the resultant force is 120 pounds.Round your answer to the nearest degree. ​