If a = 3i + 4j , b= 2i - 3j, c = - i +j, show that a +3b + 5c is parallel to x-axis.

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a= 3i + 4j

b= 2i - 3j

c= -i + j

Let us determine a+ 3b + 5c

==> a= 3i + 4j

==> 3b = 3(2i-3j)= 6i - 9j

==>5c = 5(-i+j) = -5i + 5j

Now we will add all terms:

==> a+ 3b+ 5c =...

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a= 3i + 4j

b= 2i - 3j

c= -i + j

Let us determine a+ 3b + 5c

==> a= 3i + 4j

==> 3b = 3(2i-3j)= 6i - 9j

==>5c = 5(-i+j) = -5i + 5j

Now we will add all terms:

 

==> a+ 3b+ 5c = (3i+6i-5i) + (4j-9j+5j)

                          = 4i + 0j= 4i

Since the velue of j is 0, then we conclude that the vector is parallel to the x-axis.

 

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