Two vectors, in two dimensions, are given in Cartesian coordinates as: a (8, 4) and r =(5, 2) Using these vectors, determine the vector component (a,), or part, of vector a that points in the direction parallel to vector r. In the box below, determine: a, (0, 1)
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- A farmer wants to fence off his four-sided plot of flat land. He measures three sides, shown as A, B, and D in the Figure, and then correctly calculates the length and orientation of the third side C. The length of A, B, and D are all 7.06 km. Their angles theta1, theta2, and theta3 are all 2.16 degrees. What did he find as the magnitude of C (in unit of km)?Let’s practice drawing some vectors. One the axes below, start at the origin and draw the givencomponent vectors and the resultant vector. Each line is one unit (a) |vx| = 2, |vy | = 3Three points, A, B, and C, exist on an XY-plane. The positions of points A and B are (3,1) and (1,-1) respectively. The position of point C is (-1, 3). Determine the position vector from point A to point C. Determine the unit vector for this position vector.
- Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular to plane PQR . P(-1,1,0), Q(0,0,1), R(0,0, – 1)Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular to plane PQR. Р(- 1,1, - 2), Q(-2,0,1), R(0, -2, - 1)If vectors A = (4.5, -2.5) and B = (3, 6), what is C = 2A – B?
- Jungle gym, dot products, unit vectors. A coordinate system is laid out along the bars of a large 3D jungle gym (the figure below). You start at the origin and then move according to the following steps. For each step, the distance (in meters) and direction in which you move are given by the cross product A x B of the given vectors A and B. For example, the first move is 18 m in the +z direction. What is the magnitude dnet of your final displacement from the origin? (a) A = 3.0î, B = 6.0ĵ → (b) A = - 4.01, B = 3.0k (c) A = 2.0₁, B = 4.0k (d) A = 3.0), B = - 8.01 (e) A = 4.0K, B = - 2.0î (f) A = 2.01, B = - 4.0j f XWhat is the angle θDθDformed by D⃗ (from the picture) and the +x+xaxis? Use counterclockwise to denote positive angles. Answer with 2 significant figures.The vector from the origin to point A is given as (6, -2,-4), and the unit vector directed from the origin toward point B is (2,-2, 1)/3. If points A and B are ten units apart, find the coordinates of point R
- 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?Give a vector parametric equation for the line through the point (5, 3,0) that is parallel to the line (-3 – 4t, 5t – 2, 5 – 4t): L(t) = (Enter your answer as )In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0, -3), B=(-2,5,1), and =(3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas. ▸ Part A ▸ Part B Part C -A+B-C-(0,4,3) Submit 15. ΑΣΦ Part D * Incorrect; Try Again; 9 attempts remaining 3A-2C - Previous Answers Request Answer 195] ΑΣΦ ? BHO ?