Question 665255
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
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a – b:
1 - 2 = -1
1 - (-1) = 2
--> -i + 2j
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(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(i^2 + j^2)}}}
a: {{{Mag = sqrt(1 + 1) = sqrt(2)}}}
b: {{{Mag = sqrt(5 + 1) = sqrt(5)}}}
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(d) Find the scalar product a•b
a•b = 1*2 + 1*-1 = 1
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(e) Find the orthogonal projection of vector a onto vector b. That is, find the vector projb a
That's the dot product, = 1