Question

Please help me on problem 22 and 26.

Thank you!

22. D=(3,4,0). Sketch D and find the "shadows" of D on the coordinate planes. 23. A=(1,0,0). Sketch A and find three nonparallel vectors that are perpendicular to A . How many vectors are perpendicular to A ? vectors are perpendicular to B ? 25. C = (1,2,0). Sketch C and find two nonparallel vectors that are perpendicular to C. 26. C = (0,2,3). Sketch C and find two nonparallel vectors that are perpendicular to C.

Answer 1

please see the attached images for complete solution.

22) Given that D= <3,4,07 can be written as B = 3 + 4 + o r and we know that the corespones presents the shadows of a on co-ordinates planes. Shadow on x-y plane is magnitude of 3 itu; | 139 +44) = 132742 - Jos = 5. Shadow on y-Z plane is magnitude of up tok Tuņ+ ok) = Ju2+62 = 36-4 Shadow on z-y plane is magnitude of 3itok 18 + ok l = Ja²to2 = g = 3

2 C = (0,2,3) Since, the vector lies in Y - Z plane, any vector perpendicular to 7-2 plane will be perpendicular to C. I vector: 5 i ( It may be a ² where x is real number). we can find other vector in yoz plane which is perpendicular to c. I vector: 3 - 2 RÉ (Dot Product must be zeso).