SOLUTION: Can someone please help me with this i really don't know how to do vectors, i have tried part a but i dont know if its right. Consider the two vectors a = î + ĵ and b = 2î –

Algebra ->  Vectors -> SOLUTION: Can someone please help me with this i really don't know how to do vectors, i have tried part a but i dont know if its right. Consider the two vectors a = î + ĵ and b = 2î –      Log On


   

Question 665255: Can someone please help me with this i really don't know how to do vectors, i have tried part a but i dont know if its right.
Consider the two vectors a = î + ĵ and b = 2î – ĵ .
(a) Calculate a + b and a – b .
a + b = 2 î^2 + ĵ^2
a – b = 2
(b) On a Cartesian plane, illustrate the vector addition a + b and the vector subtraction a – b. Clearly label your diagrams with all its appropriate vectors.
(c) Calculate the magnitude of a and the magnitude of b.
(d) Find the scalar product a•b.
(e) Find the orthogonal projection of vector a onto vector b. That is, find the vector projb a .
Found 2 solutions by lynnlo, Alan3354:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
ok,go to vector.com/math because it will give you plenty of
examples to help you understand all types of your problems

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the two vectors a = i + j and b = 2i - j
(a) Calculate a + b and a – b
a + b:
2 + 1 = 3
1 - 1 = 0
--> 3i
==========================
a – b:
1 - 2 = -1
1 - (-1) = 2
--> -i + 2j
================
(b) On a Cartesian plane, illustrate the vector addition a + b and the vector subtraction a – b. Clearly label your diagrams with all its appropriate vectors.
(c) Calculate the magnitude of a and the magnitude of b
Mag+=+sqrt%28i%5E2+%2B+j%5E2%29
a: Mag+=+sqrt%281+%2B+1%29+=+sqrt%282%29
b: Mag+=+sqrt%285+%2B+1%29+=+sqrt%285%29
-----------------------------------
(d) Find the scalar product a•b
a•b = 1*2 + 1*-1 = 1
--------------------------
(e) Find the orthogonal projection of vector a onto vector b. That is, find the vector projb a
That's the dot product, = 1