QUICK CHECK 4 Consider the equation of a plane in the form n· P„P = 0. Explain why the equation of the plane depends only on the direction, not on the length, of the normal vector n. <
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- Parameterize the plane through the point (1,−3,−2) with the normal vector ⟨−5,−2,5⟩ r⃗ (s,t)=? Use ss and tt for the parameters in your parameterization, and enter your vector as a single vector, with angle brackets: e.g., as < 1 + s + t, s - t, 3 - t >.)example of a vector equation for a line in 3 dimensions which doesn’t intersect the plane at z = 0Fine the Vector function that represents the curve of intersection of the two surfaces. The cone z= Square root x^2+y^2 and the plane z=1+y
- Consider the plane passing through the point (2, 0, −1) with normal vector (1, 1, 1). Consider a line passing through the points (1, 5, 1) and (2, 4, 1). Find the point of intersection with the plane, or if the line is parallel to the plane, find the point of distance between the plane and the line. Do so by hand, without any graphical utilities.Determine the scalar equation of a plane with normal vector ? = [3, 1, 3] that has a y-intercept of 5.What is a curve’s binormal vector? Give an example. How is this vector related to the curve’s torsion? Give an example.
- Find the point where the line through the origin and perpendicular to the 2x - y - z = 4 plane intersects the 3x - 5y + 2z = 6 plane. Assume that n is normal to a plane and that v is parallel to the same plane. Describe how you would find a vector n that is both perpendicular to v and parallel to the planeDetermine the equation of the plane with a point 'a' and the normal vector 'n': a = (−1, 2, −3)t , n = (2, 4, −1)t Please show how you do this step by step, which formula do I use, how do I visualise this?Surface area of a helioid with vector equation.
- If false explain why. Justify your answer. True or False: “Let L be a line in R3 with direction vector d, and let P be a plane with normal vector n. If n · d = 0, then P and L intersect.”Transforming vector filed in Cartician coordinate to Cylindrical coordinate, how to find its direction?certain plane is described by 2x + 3y + 4z = 16. Find the unit vector normal to the surface in the direction away from the origin can you include a diagram please and specify all the vector with an arrow ???