Doubt from vectors

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How to approach these type of questions

If you want i shall upload proof of AB/AC=BD/DCScreenshot_2019-10-24-12-05-33-1

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@Hari_Shankar Sir, do you have any different approach.

I think using the section formula is the simplest wayIMG_20191024_134930

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Yeah, sir great approach. Totally forgot about this one.

Screenshot_2019-10-24-14-43-39-1 proof of ratio...

Screenshot_2019-10-24-15-00-14-1

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IMG_20191025_182920
Q 22

Is ans a?

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Oh sorry , i have to ask another. I am posting that

15720096791252558808797021573162
Q 4

2019_10_25%2018_53%20Office%20Lens

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Is it multiple option question?

Answer for 4 is option A, BIMG_20191025_191212

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Answer mentions option a only

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Q 17 and Q 20

Screenshot_2019-10-26-20-35-58

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Screenshot_2019-10-26-20-36-40 trying to solve in other shortest way

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@Hari_Shankar sir @Jagdish_Singh sir @Sneha_2021 Please see for a shorter approach