Find the curve describing a straight line going through the points P:(1,1,1) and Q :(-3,4,1) Hint:...
Let l denote the line through the origin with direction vector (1,1,1). Let r(t) = (t +1,4, 2t) be a parametrized curve. Compute the point r(to) on the curve which is closest to l, and state the distance from r(to) to l.
Q2. Let u and v be non-parallel vectors in Rn and define Suv (a) Does the point r lie on the straight line through q with direction vector p? (b) Does the point s lie on the straight line through q with direction vector p? (c) Prove that the vectors s and p -r are parallel. (d) Find the intersection point of the line {q+λ p | λ E R} and the line through the points u and v. Q3....
Find the three angles of the triangle with the given vertices: P(1,1,1), Q(1,−5,2), and R(−2,2,6) Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)
Show that a straight supply curve going through the origin has the price elasticity of supply equals to 1 at every point. (Hint: assume a function of P=aQ+b where a>0 and b=0)
The figure below shows a curve C, parametrized by (a) The point P lies on C, and its r-coordinate is 4. Find the value of t at the point P according to the parametrization, and find the y-coordinate of P. equation in terms of r and y. line 4. as shown shaded in the figure. Find the area of R. (b) The line is normal to C at the point P. Express the line l using an (c) The bounded...
Find the line integrals of F=3yi + 4xj + 2zk from (0,0,0) to (1,1,1) over each of the following paths. a. The straight-line path Cy: r(t) = ti + tj + tk, Osts 1 b. The curved path Cz: r(t) = Osts1 c. The path C, UC, consisting of the line segment from (0,0,0) to (1,1,0) followed by the segment from (1,1,0) to (1,1,1) (0,0,0) (1.1.1)
- PLEASE SHOW ALL STEPS - PLEASE ANSWER ALL PARTS FOR THE QUESTION Find a function r(t) for the line passing through the points P(0,0,0) and Q(3,4,1). Express your answer in terms of i, j, and k. r(t) = 3ti + + k, for
Find a vector parametric equation F(t) for the line through the points P= (1,1, 4) and Q = (-2,-2,8) for each of the given conditions on the parameter t. (a) If 7(0) = (1,1, 4) and 7(5) = (-2,-2,8), then F(t) = HI (b) lf F(7) = P and 7(11) = Q, then F(t) = HI -2, respectively, then (C) If the points P and Q correspond to the parameter values t = 0 and t F(t) =
4. Let point P(2,1,12) and Q be points on the curve r(t)=(5-31, 41-3,12t). Find the coordinates of point Q such that the arc length of curve r from P to Q is 4 units. Write your final answer as an ordered triple.
4. Let point P(2,1,12) and Q be points on the curve r(t)= (5 – 31,4t – 3,12t). Find the coordinates of point Q such that the arc length of curve r from P to Q is 4 units. Write your final answer as an ordered triple.