Answered: 1. A particle moves so that it's… | bartleby

Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.3: Vectors In The Plane

Problem 10ECP

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1. A particle moves so that it's position vector is
given by i = cos wtî + sin wtĵ , where w is a
constant. Show that
(a) The vector of the particle i is perpendicular to 7
(b) 7 x ở = a constant vector

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(14) The straight line L passes through the origin O and is in the direction i+mj. The straight line L' passes through the point A whose position vector is ai and is in the direction i+m'j. Write down the vector equations of L and L' and find the position vector of their point of intersection.
calculate speed only, the rest are done.
Sketch the curve with the vector equation r(t) = cos(t)i − cos(t)j + sin(t)k. Show the direction of increasing t with an arrow drawn on your curve.
Sketch the curve whose vector equation is Solution r(t) = 6 cos(t) i + 6 sin(t) j + 3tk. The parametric equations for this curve are X = I y = 6 sin(t), z = Since x² + y² = + 36. sin²(t) = The point (x, y, z) lies directly above the point (x, y, 0), which moves counterclockwise around the circle x² + y2 = in the xy-plane. (The projection of the curve onto the xy-plane has vector equation r(t) = (6 cos(t), 6 sin(t), 0). See this example.) Since z = 3t, the curve spirals upward around the cylinder as t increases. The curve, shown in the figure below, is called a helix. ZA (6, 0, 0) (0, 6, 37) I the curve must lie on the circular cylinder x² + y² =
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The position vector of a particle is r(t). Find the requested vector. 5) The acceleration at t = for r(t) = (4 sin 41)i - (10 cos 41)j + (5 csc 41)k 5) A) = -64i + 80k B) a = -64i - 80k 8 = 64i + 80k 160j + 80k
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