What is the sum of the squares of direction cosines of the line joining the points (1,2,-3) and (-2,3,1)?

Options

A. 0
B. 1
C. 3
D. `2/sqrt26`

Answer

B

Explanation

Let the direction cosines be l, m, n
Let `P(x_1,y_1,z_1) and Q(x_2,y_2,z_2)` be two point which joins a line.
`:. X_1=1,y_1=2,z_1=-3`
`x_2 =-2,y_2=3,z_2=1`
Now, `l=(x_2-x_1)/sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`
`=(-3)/sqrt26`
`m=(y_2-y_1)/sqrt((x_2-x_1)^2+(y_2-y_1)+(z_2-z_1)^2)=1/sqrt26`
`n=4/sqrt26`
`:.l^2+m^2+n^2=9/26+1/26+16/26=26/26=1`
Always equal to 1