Find a vector perpendicular to both 7 = 2î + +5k and w=4ỉ – 2j+k a)...
8. Find a vector perpendicular to both $22î +j+5k and 121 49 – 2j+k a)3î +79-6kb) 11î +18) - 8 c) 4 - 8ì+ỉ d)î +99 - 3Ã e) none of these
if
v=-4i+2j and w=2i-3j then find
a= v+w
b=b-w
c=3v
d=2v+2w
7. If v =-4i+ 2j and w = 2i - 3j. Then find (Section 7.6) a. vw b. v -w C. 3v d. 2v2w
14. A vector that is normal to the graph of z=x² + y2 +7 at the point (2,1,12) is a) 4ỉ +29 – Ã b) î–2j+3ỉ c) 7î++4k d) – 6 –2j + k e) none of these
1- Two vectors are given as u = 2î – 5j and v=-î +3j. a- Find the vector 2u + 3v (by calculation, not by drawing). (4 pts) b- Find the magnitudes lil and 17% of the two vectors. (4 pts) c- Calculate the scalar product uov. (5 pts) d- Find the angle 0 between the vectors ū and . (6 pts) e-Calculate the vector product u xv. (6 pts)
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal to a and b. _ [3 marks] (b) Show that the vector from (a) is orthogonal to a and b. [1 mark]
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a) 30 - 5V._b) 2V - W'. 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculato
question about linear algebra
21. The following two lines := -i+j+ k + t(2i - 2j - 2k), t e R r and y2 1 = 2 -1 intersect each other. What is the equation of the line (where s E R) passing through the intersection point of these two lines and perpendicular to both of them? r -ijk s(i - j - k) (a) (b) r i2j+3k + s(i - 2j + 7k) (c) (d) rsik) (e) =j-k s(i...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
7. (9 pts) Find a vector perpendicular to the plane containing the triangle whose vertices are (1, 3, 2), (4, –2, 1), and (2, 3, –1)
If a vector K?? ? has components Kx= 5.9 and Ky = -13, then find the magnitude K and direction Theta (as a positive rotation angle relative to the +x-axis) of the vector. 6. K a. 9.915 b. 7.177 c. 12.04 d. 14.28 e. 15.11 f. 24.14 7. Theta a. 565° b. 581.1° c. 343° d. 391° e. 294.4° f. 452.1°