My question is from the beginning of the book, Chapter 1, problem 1.2 How do you

Question

My question is from the beginning of the book, Chapter 1, problem 1.2

How do you get the dot product of a vector "r" (4.000i - 1.000j) and a unit vector "u" (0.8319i - 0.5546j)??? The solution manual shows...                          
[(4.000i - 1.000j)ft] *(dot product)* (0.8319i - 0.5546j) = 3.822 ft
I am having difficulty understanding the multiplication of this. When I attempted this, I multiplied 4.000i times 0.8319i, which an "i" cross an "i" is zero. So then I did 4.000i times -0.5546j. Since 'i' cross 'j' is 'k' and it is negative, I got -2.2184k. Then I did -1.000k times 0.8319i and got 0.8319k since 'j' cross 'i' is negative 'k', but the negative 'j' turns it to a positive 'k'. So from there I was left with -2.2184k + 0.8319k = -1.3865k
So what is it that I am doing wrong since I did not get the answer 3.822???


How do you get the dot product of a vector "r" (4.000i - 1.000j) and a unit vector "u" (0.8319i - 0.5546j)??? The solution manual shows...                          
[(4.000i - 1.000j)ft] *(dot product)* (0.8319i - 0.5546j) = 3.822 ft
I am having difficulty understanding the multiplication of this. When I attempted this, I multiplied 4.000i times 0.8319i, which an "i" cross an "i" is zero. So then I did 4.000i times -0.5546j. Since 'i' cross 'j' is 'k' and it is negative, I got -2.2184k. Then I did -1.000k times 0.8319i and got 0.8319k since 'j' cross 'i' is negative 'k', but the negative 'j' turns it to a positive 'k'. So from there I was left with -2.2184k + 0.8319k = -1.3865k
So what is it that I am doing wrong since I did not get the answer 3.822???

Explanation / Answer

In dot product i.i = j.j=1 i.j=j.i =0 so (4.000i-1.000j) .(0.8319 i-0.5546 j) = (4.000 x 0.8319) + (1.000 x 0.5546) = 3.8822 ft ANS; It is a dot product ; you did it as a cross product. i think that yourdoubt is clarified.

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