MCQ practice · SSC Higher Mathematics Board questions · Chapter 12: Planar Vector
If the position vectors of A, B, C are a⃗, b⃗, c⃗ respectively and C divides the segment AB internally in the ratio 2 : 3, what is c⃗?
Think it through first, then pick an option.
- a (3b⃗ + 2a⃗)/5
- b (2b⃗ + 3a⃗)/5
- c 3b⃗ − 2a⃗
- d 2b⃗ − 3a⃗
Answer and explanation
Correct answer: b (2b⃗ + 3a⃗)/5
For 2 : 3, c⃗ = (2b⃗ + 3a⃗)/5; for m : n the weight of b is m and of a is n.
Why the other options are wrong
- a (3b⃗ + 2a⃗)/5: The weights are swapped in (3b⃗ + 2a⃗)/5: for the ratio 2 : 3 the weight of b is 2 and of a is 3.
- c 3b⃗ − 2a⃗: 3b⃗ − 2a⃗ lacks the denominator and has the wrong sign; internal division adds and divides by m + n.
- d 2b⃗ − 3a⃗: 2b⃗ − 3a⃗ lacks the denominator and has the wrong sign; internal division gives (mb + na)/(m + n).
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