How do you find a vector of length 10 that is oppositely directed to u=3i-4j?

1 Answer
Shwetank Mauria
Jul 14, 2016

A vector of length #10# that is oppositely directed to u=3i-4j is #-6i+8j#

Explanation:

A vector oppositely directed to #u=3i-4j# is #v=-u=-(3i-4j)# i.e. #v=-3i+4j#.

However, its length is given by #|v|=sqrt((-3)^2+4^2)=sqrt(9+16)=sqrt25=5#

What we desire is a vector of length #10# that is double of #v# and hence

A vector of length #10# that is oppositely directed to u=3i-4j is #2v=2*(-3i+4j)=-6i+8j#

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