Question

The direction ratio of the line joining the points $(4,3, - 5)$ and $( - 2,1, - 8)$ are
A. $\left(\dfrac{6}{7},\dfrac{2}{7},\dfrac{3}{7}\right)$
B. $(6,2,3)$
C. $(5,8,0)$
D. $(3,7,9)$

Answer 1

Hint: We have to find the direction ratio of the line joining the points $(4,3, - 5)$ and $( - 2,1, - 8)$.First, we will assume given points as A and B. Then we will use the concept Direction ratio= Position vector of A – Position vector of B to get the direction ratio of the line joining the points $(4,3, - 5)$ and $( - 2,1, - 8)$.

Formula Used: Direction ratio=\[({x_2} - {x_1},{y_2} - {y_1},{z_2} - {z_1})\]

Complete Step by step solution: We have given two points
Let $A(4,3, - 5)$ and $B( - 2,1, - 8)$
Direction ratios can be defined as vector components along x-axis, y-axis and z-axis respectively, if we have a vector $(x\hat i + y\hat j + z\hat k)$ the direction ratios for the vector are $x,y,z$
Now, we will find the direction ratio of AB
Direction ratio=\[({x_2} - {x_1},{y_2} - {y_1},{z_2} - {z_1})\]
$ = 4 + 2,3 - 1, - 5 + 8$
After simplification above expression
$ = 6,2,3$

Hence, option (B) is correct.

Note: Students should take care while solving questions. And should understand the question correctly in order to get the correct answer. And should use correct concept of direction ratio which is Direction ratio=\[({x_2} - {x_1},{y_2} - {y_1},{z_2} - {z_1})\] in order to get error free solution