(1 point) Suppose a line is given parametrically by the equation L(t) = (3,2 – 3t,...
1 point) Suppose that the line l is represented by r(t)- (12+ 2t, 23 +6t, 8 + 2t) and the plane P is represented by 2x + 4y + 52-23. 1. Find the intersection of the line & and the plane P. Write your answer as a point (a, b, c) where a, b, and c are numbers. Answer 2. Find the cosine of the angle 0 between the line l and the normal vector of the plane P Answer:...
Find the distance of the point (3,4,-4) from the line r(t) = (1 + 3t, -1 + 2t, 5 – 3t). Answer:
Consider line L, given below. x = 6 + t, y = 7 + t, z = 3 + 3t, tER (a) Find point P that belongs to the line and direction vector v of the line. Express v in component form. P = V = (b) Find the distance from the origin to line L.
3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t) =t+4 12: x(u) = 5 - 3u, y(u) = u +1, (u) = u +2 1. Determine whether li and ly are parallel, skew or intersect. If the lines intersect, find the point of intersection of li and 12. 2. If the lines intersect or are parallel, give an equation for the plane which contains both lines. If the lines are skew, find a...
please answer question 4-7 Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
(1 point) Consider the line L(t) = (2+ 3t, 6-t). Then L intersects: 1. The X-axis at the point (2,6) when t = 0 2. The y-axis at the point (2,6) when t = 0 3. The parabola y = x2 at the points and when t = and
Find the equation of the plane through the point (-2,8,10) and parallel to the line x=1+t, y=2t, z=4-3t
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z = 6cos(3t); (0,71,- 6) Find the equation of the osculating plane of the curve at the given point 4x + 18y = 18 b. X + 18y = 1871 4x - y = - 1871 d. X - 18y = - 1871 x + 18y = - 1871 C. e. a Ob С Od e
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
(8 points) Find the points of intersection in R3 of the line L(t) = (3-1, -2+1, 3t) and the unit sphere: x2 + y2 + x2 = 1 (Hint: Use x = 3t - 1, y = -2t + 1 and 2 = 3t in the equation of the sphere, and solve for t.)