All 303 families

GB-34-04-001 · Parallel vector proof

Non-zero vectors are given by PQ→=9(−9a−4b)\overrightarrow{PQ}=9(-9\mathbf a - 4\mathbf b) and RS→=12(−9a−4b)\overrightarrow{RS}=12(-9\mathbf a - 4\mathbf b). Prove that PQ and RS are parallel.

Vectors: Showing Two Vectors are Parallel Booklet p. 90
Method
To show vectors are parallel, factorise and show that one vector is a non-zero scalar multiple of the other
Worked Example (GB-34-04-001)
1)
Express RS as 43\frac{4}{3} times PQ.
2)
Non-zero scalar multiples have parallel directions.
Ans = RS→=43PQ→\overrightarrow{RS}=\frac{4}{3}\overrightarrow{PQ}