Question

A student starts from the hostel and goes to his friend's house and then to his school. A is the displacement vector from the hostel to his friend's house. B is the displacement vector from his friend's house to school, and C is the direct path from the hostel to school. Which of the following vector operations is correct for the displacement from the hostel to his friend's house?
A) A - B.
B) A + B.
C) C - B.
D) C + B.

Answer 1

Answer:$\vec{C}-\vec{B}$

Explanation:

Given

$\vec{A}$ is displacement of student from Hostel to house

$\vec{B}$ is displacement of student from house to school

And $\vec{C}$ is displacement of student from Hostel to school    

According to the triangle law of vector addition  

If two vectors are acting on a body simultaneously that are shown by magnitude and direction by two sides of a triangle taken in order then the third side is the resultant of two vectors that are taken in opposite direction.

$\vec{A}+\vec{B}=\vec{C}$

$\vec{A}=\vec{C}-\vec{B}$

so option c is correct