MCQ practice · SSC Higher Mathematics Board questions · Chapter 12: Planar Vector
If OA⃗ = a⃗, OB⃗ = b⃗ and AC = BC, what is OC⃗?
Think it through first, then pick an option.
- a (a⃗ − b⃗)/2
- b b⃗/2 − a⃗
- c a⃗/2 − b⃗
- d (a⃗ + b⃗)/2
Answer and explanation
Correct answer: d (a⃗ + b⃗)/2
AC = BC means C is the midpoint of AB; so OC⃗ = (a⃗ + b⃗)/2.
Why the other options are wrong
- a (a⃗ − b⃗)/2: (a⃗ − b⃗)/2 is a half of −AB⃗; for a midpoint a and b are added.
- b b⃗/2 − a⃗: In b⃗/2 − a⃗ the coefficient of a is −1, which is not the midpoint formula.
- c a⃗/2 − b⃗: In a⃗/2 − b⃗ the coefficient of b is −1, which is not the midpoint formula.
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