Find the value of |p| and the value of|q|

Question

The vector P is a multiple of the vector 3i + j and vector q is a multiple of 2i + j. Their difference p - q is a multiple of the vector 4j + 3j. Given that |p - q| = 10. Find the value of |p| and the value of|q|

Answer 1

Given p=m(3i+j), q=n(2i+j), p-q=k(4i+3j), |p-q|=10, where m, n and k are scalar constants. Vectors are shown in bold.

k√(4²+3²)=5k=|4ki+3kj|=10⇒k=2, p-q=8i+6j.

p-q=(3m-2n)i+(m-n)j; 3m-2n=8, m-n=6, so m=n+6, therefore 3(n+6)-2n=8, 3n+18-2n=8⇒n=-10, m=-4.

p=-12i-4j, q=-20i-10j.

|p|=√(144+16)=√160=4√10; |q|=√(400+100)=√500=10√5.

Comments

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