NIMCET 2016 Mathematics Question 2 with Solution

Question 2

Mathematics Scalar and Vector Products Hard

If C is the midpoint of AB and P in any point outside AB, then

(A) \(\overline{PA}+\overline{PB}=2\overline{PC}\)

(B) \(\overline{PA}+\overline{PB}=\overline{PC}\)

(C) \(\overline{PA}+\overline{PB}=2\overline{PC}=0\)

(D) \(\overline{PA}+\overline{PB}=\overline{PC}=0\)

View Dynamic Solution & Explanation ▼

Correct Solution: Option A

Step-by-step Solution:

Here is the MathJax representation of your given vector equations: \[ \overrightarrow{PA} = \overrightarrow{PC} + \overrightarrow{CA} \] \[ \overrightarrow{PB} = \overrightarrow{PC} + \overrightarrow{CB} \] \[ \overrightarrow{PA} + \overrightarrow{PB} = 2\overrightarrow{PC} + (\overrightarrow{CA} + \overrightarrow{CB}) \] \[ = 2\overrightarrow{PC} \quad (\because \overrightarrow{CA} = -\overrightarrow{CB}) \] \[ \text{Hence } \overrightarrow{CA} + \overrightarrow{CB} = 0 \] \[ \text{and } \overrightarrow{PA} + \overrightarrow{PB} = 2\overrightarrow{PC} \]