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    Can someone please explain the following question? Thanks a bunch....

    Q: Given that a = 2i + 5j and b = 3i - j, find:
    a) lambda if a+lambda(b) is parallel to the vector i
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    (Original post by Hamoody96)
    Can someone please explain the following question? Thanks a bunch....

    Q: Given that a = 2i + 5j and b = 3i - j, find:
    a) lambda if a+lambda(b) is parallel to the vector i
    You need to find \lambda such that 2i + 5j + 3\lambda i - \lambda j = i(2 + 3\lambda) + j(5 - \lambda) = k(i + 0j) = ki + 0j (this is because if two vectors are parallel they need to be a multiple of one another)

    So you can equate the j components and find lambda.
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    (Original post by Zacken)
    You need to find \lambda such that 2i + 5j + 3\lambda i - \lambda j = i(2 + 3\lambda) + j(5 - \lambda) = k(i + 0j) = ki + 0j (this is because if two vectors are parallel they need to be a multiple of one another)

    So you can equate the j components and find lambda.
    Ok hold on a second...
    I didnt understand what you did in the third step with the k... Why did you do that? Annnd what do we do when two vectors are parallel to each other again?
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    (Original post by Hamoody96)
    Ok hold on a second...
    I didnt understand what you did in the third step with the k... Why did you do that? Annnd what do we do when two vectors are parallel to each other again?
    If you have two vectors a_1 i + b_1 j and a_2 i + b_2 j then they are parallel if

    there exists some real number k such that a_1 i + b_1 j = k(a_2 i + b_2 j)

    or equivalently that we have some real number k such that a_1 = ka_2 and b_1 = kb_2.

    In your case, for a  + \lambda b to be parallel to the vector i = 1 i + 0 j then we need to be able to write a + \lambda b = k(1 i + 0j).

    Then we equate the components to find lambda, finding that we only need to care about the j components.
 
 
 
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