Draw a vector that represents a displacement of 40 miles east. Then, from that point, draw one that represents a displacement of 30 miles north. Sketch in the resultant vector. Using the Pythagorean theorem and the tangent function, solve for the magnitude and direction of the resultant.

A vector v has initial point P₁ = (-1,2) and terminal point P₂ = (x, 14). Find all numbers x so that v has length 13. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list if needed.) X=

can i have the answer to this table using degree + direction (EX. 20degrees East) Thank you very much! (P.S sorry i didn't upload the picture)

Given the vector techniques you worked on in the lab, answer the follow question: suppose you first walk 12 m in a direction 20° west of north, then 20 m in a direction 40° south of west, then 14 m in a direction 30° east of north, and finally 19 m in a direction 40° east of south.  How far are you (as the crow flies) from your starting point, and what is the compass direction (west of south) of a line connecting your starting point to your final position?

In the next sets, you are given the magnitude and one component. There is an ambiguity in determining the vector, because you can only determine the absolute value of the other component and not its sign; therefore, there are two possibilities. In these tables, you must enter the absolute value of the component and provide two angles for the vector, the first one assuming the other component is positive and the other assuming the component is negative. You must also provide two angles for the antiparallel vector in the same order. Set Set 5a 5b 6a 6b Ax |Axl 32 -26 Ayl Ay SENECIENTE 42 -21 Magnitude of A 62 62 Magnitude of A 72 64 Angle of A Angle of A 0 0 (pos A) (neg Ay) (pos Ay) (neg Ay) (pos A) (neg Ax) (pos A) (neg Ax) Angle of -A Angle of -A 0 0 (pos Ay) (neg A,) (pos Ay) (neg Ay) (pos A) (neg Ax) (pos A) (neg A₂)

Bruce begins 7 kilometers to the north of town and rides his bike along a straight trail which leads to a park 3km west of town. It takes him 20 minutes to cover this distance. Write a vector in component form that describes his ride while also finding the magnitude and direction of this vector. Also, find the component of Bruce's motion which is in the direction of SW using a unit vector that uses both forms of the dot product (algebraic and geometric), then write parametric equations expressing his motion with the town being represented by the origin and t=0 being his starting point. Using these equations, what is his position after 5 minutes? Then eliminate the parameter to get a rectangular equation for this linear path and verify algabraically amd graphically that this equation represents the line.

I'm thinking it is due east and 310 newtons for the first part. Due to adding forces together, the second part being 140 newtons going east showing the additional force. Am I thinking about this the wrong way? This is a practice problem.

Question: True or False. Why? A vector space must contain at least two vectors. My Comment: I'm confused why this is a question because I believe it to be False. If I draw one vector on a graph with the coordinates (3,5), it is taking up a vector space on an xy coordinate system. Is that incorrect?

could you explain how to solve this?

plesae circle and label answers.