Find parametric equations for the line described below.The line through the point P(5, -5, 1) parallel to the vector  -3i + 4j – 6k. 

Find the requested vector.v = 5i + 3j + k, u = 4i + 5j – 3kFind a vector orthogonal to both v and u. Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  Be sure to use vector notation!  (Either use component form or i, j, k form.) 

What is the difference between something having inherent or intrinsic value, compared to having instrumental or extrinsic value?Think of, discuss/explain an issue in the area of environmental ethics in which this distinction would be an important/influential one (= an environmental issue for which the difference between inherent and instrumental value would make a significant difference in how we viewed/analyzed that issue).*** Remember that copying/pasting from any course materials (other than your own words in the Prep Guide), the internet, or using generative AI like ChatGPT to help “write” or “proofread” or “improve” your answer violates my Academic Integrity policy. Note that generative AI is now incorporated into many popular writing and translating platforms (e.g. Grammarly, Quillbot, Google Translate, DeepL, etc.), so if you’re using those platforms, you’re using generative AI in violation of my policy. USE YOUR OWN WORDS or, if you are unable to do that, properly quote/informally cite them as I discuss in the Academic Integrity section of the Syllabus ***  

Find the unit vector that has the same direction as the vector v.v = 4i – 3j

Write the equation for the plane.The plane through the points P(-1, 4, -23) , Q(2, 2, 2) and R(1, -6, 11)

Find the distance from P1 to P2.P1 = (1, 0, -2) and P2 = (3, 2, 4)

Find the specified vector or scalar.u = 4i + j and v = 8i + j; Find  | u + v | . Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Find the center and radius of the sphere.x2 + y2 + z2 – 12x – 14y + 2z = -5 Center:  ( [xvalue], [yvalue], [zvalue] ) Radius:  [radius]

Solve the problem.A pilot wants to fly on a bearing of N 62.7° E. By flying due east, he finds that a 55-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane.

Solve the problem. (Give your answer as a terminating decimal.)Find x so that the vectors v = i + xj and w = -3i + 5j are orthogonal.