Vectors and similar triangles problem

[LiHJ]

Homework Statement

Dear Mentors and PF Helpers,

Here's the question:

Homework Equations

The Attempt at a Solution

Here's my solutions:

Please let me know whether I'm right. Thank you

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[NascentOxygen]

Hi LiHJ. How would you justify saying PQ is half the length of SR?

Edit: the rest looks right, though you are a bit rough & ready with the geometry. PQRS shouldn't be designated using the Δ symbol! :)

 

[LiHJ]

Because the question mention that Q is the midpoint of OR and PQ is parallel to SR. So triangle OPQ is similar to triangle OSR. Therefore P is a midpoint of OS

 

[LiHJ]

Thank you;)