Consider the points P(0,0,9) and Q(-3,3,0). a. Find PQ and state your answer in two forms:...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
Consider the vectors A = 2.0i - 4.0j + k. B = 3.0i + 4.0j + 10.0k, C = -3.0i - 4.0j, D= -3.0i +4.0j, E = -2.0i + 3.0j +2.0k, F=-9.0j.Part (a) What is A × B? Give your answer in the form of "ai + bj + ck". Part (b) What is B × A? Give your answer in the form of "ai + bj + ck". Part (c) What is C × D? Give your answer in the form of...
Express Fas a vector in terms of the unit vectors i, j and k (present your answer with 3 significant figures). Please enter your answers in the form of Ai +Bj +Ck. z - F = 60 N 1101 40 50 Dimensions in millimeters Determine the angle in degrees between F and the y- axis. z - F = 60 N 1101 40 50 Dimensions in millimeters 300 mm 150 mm 200 mm Use the vector product treatment to express...
Let P and Q be two projectors, such that PQ zQP prove that (PQ) is a projector and (a) CLPQ) = c(p). ndo) (6) Null (PQ) = Null P + Null Q
Fourth Homework (1) Let P-(**.0) and Q ( . (a) Find the pole of the line PQ (b) Find the parametrization of the line PQ (c) Does (ch,顽週lie on the line PQ? 克,2 7, ) lie on the line PQ? (2) Find the distance between the lines (1,0,-1) + t(2,3,0) and m (2,-1,3) +s(0, 1,2). (3) Let A and B be two distinct points of S2. Show that X e I d(X, A) = d(X, b)) is a line and...
For the points P(3.4) and Q(3,5), find (a) the distance between P and Q and (b) the coordinates of the midpoint of the segment PO. (a) The distance between P and Q is, d(P,Q) = (Simplify your answer. Type an exact answer, using radicals as needed.) (b) The midpoint of the segment PQ is (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed.)
Question number 46 please.
cluls paae to v with three times the magnitude of v 40. Which has the greatest magnitude, 2 u or 7 v? 41. Which has the greater magnitude, u v or w-u? 42-47. Unit vectors Define the points P(-4, 1), 03, -4), and R2, 6) 42. Esxpress P0 in the form a i + b j Express PO in the form ai+ bj 43. Express OR in the form a i + b j 44. Find...
Question 13 (8 points) If logb(p)=91 and logb(q)=54, then determine logb(pq). Your Answer: Question 13 options: Answer Question 14 (8 points) If logb(R)=628 and logb(X)=4, then determine logb(R/X). Your Answer: Question 14 options: Answer
(a) Find a unit vector that is orthogonal to the plane through the points P(0,0,–3), Q(4,2,0), and R(3,3,1) (b) Find two non-parallel vectors that are orthogonal to the vector Ŭ = i + 2) + 3k (c) Find the angel between the vector Ở = 51 + 21 – k and the z - axis (d) Describe why it is impossible for a vector to have the following direction angles 511 6 -, B = 3, and y TT π...
3. (RSA) Consider N-pq where p- 3 and q 5. (a) Calculate the value of N p. N 15 (b) Let c 3 be the encoding number. Verify that c satisfies the require- ments of an encoding number (c) Find the decoding number d. [Hint: cd Imod(p 1)(q 1).] 3dI mod 2 (d) Consider the single character message 'b' (not including the quotes) Using its ASCII code it becomes the numerical plaintext message " 98 Calculate the encrypted message ba...