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A2 Pure Maths-vector magnitude

My question says:

Find a vector of magnitude 27 units which is paralell to 3i + 4j .

I understand that for the vector to be paralell it would have to be like 6i + 8j , 9i +12j etc etc but how do I find the magnitude of the vector?

Is finding the modulus finding the magnitude?? (i.e. the square root of (3^2 + 4^2) would find the magnitude of the original vector?)

Im not sure if this post makes much sense, but please help if can!!! thanks x

Reply 1

freemyice

let the new vector be u(3i + 4j)
so the squre of the magnitude of the vector is (3u)^2 + (4u)^2 =25u^2=27^2
==>u^2=27^2/25
so u=+ 27/5
=> the new vector is + 27(3i+4j)/5

Reply 2

yazan_l

another way: find unit vector of the vector: u have:
magnitude of 3i+4j = |3i+4j| = (3²+4²)^.5 = 5
unit vector = (3i+4j)/5
so the new vector = unit vector * new magnitude = 27(3i+4j)/5