NIMCET 2016 Mathematics PYQ — If C is the midpoint of AB and P in any point outside AB, then… | Mathem Solvex | Mathem Solvex
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NIMCET 2016 — Mathematics PYQ
NIMCET | Mathematics | 2016
If C is the midpoint of AB and P in any point outside AB, then
Choose the correct answer:
A.
PA+PB=2PC
(Correct Answer)
B.
PA+PB=PC
C.
PA+PB=2PC=0
D.
PA+PB=PC=0
Correct Answer:
PA+PB=2PC
Explanation
Concept: When vectors are added, the sum can be found out graphically. The process is:
• Draw a line representing a vector and the line length is equal to the magnitude of a vector. • Draw the other vector to be added by other lines in a way that the head of the previous one joins to the tail of the next. • Draw all the vectors to be added in a similar way. • When all the vectors to be added are drawn, the summation is the line joining the tail of the first vector to the head of the last vector.
Calculation:
As per the diagram, PC+CA=PA ........(i) PC+CB=PB ........(ii)
Adding the 2 equations (i) and (ii), we get, 2PC+CA+CB=PA+PB ........(iii)
Given that C is the mid-point of AB, then ∣CA∣=∣CB∣
But, directions are opposite so, CA=−CB ........(iv)
By equations (iii) and (iv), 2PC+(−CB)+CB=PA+PB
⇒2PC=PA+PB
Explanation
Concept: When vectors are added, the sum can be found out graphically. The process is:
• Draw a line representing a vector and the line length is equal to the magnitude of a vector. • Draw the other vector to be added by other lines in a way that the head of the previous one joins to the tail of the next. • Draw all the vectors to be added in a similar way. • When all the vectors to be added are drawn, the summation is the line joining the tail of the first vector to the head of the last vector.
Calculation:
As per the diagram, PC+CA=PA ........(i) PC+CB=PB ........(ii)
Adding the 2 equations (i) and (ii), we get, 2PC+CA+CB=PA+PB ........(iii)
Given that C is the mid-point of AB, then ∣CA∣=∣CB∣
But, directions are opposite so, CA=−CB ........(iv)
