How do you write the vector equation that passes through point (-1,4) and parallel to <6,-10>?

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Answer 1 · 2017-01-17T15:52:35

# vec(r) = ( (-1), (4) ) + lamda ( (6), (-10) )#

The vector equation of a line in the direction of #vec(D)# passing through the point #vec(A)# is:

# vec(r) = vec(A) + lamda vec(D) #

So the required equation in vector form is:

# vec(r) = ( (-1), (4) ) + lamda ( (6), (-10) )#

Alternative notations are:

# vec(r) = <<-1, 4>> + lamda <<6,-10>> #

Or,

# vec(r) = (-1hat(i)+4hat(j)) + lamda (6hat(i)-10hat(j)) #