A line passes through two points A(2, -3, -1) and B(8, -1, 2). The co-ordinate of a point on this line at a distance of 14 units from A are :

A. (14, 1, 5)

B. (86, 25,41)

C. (-10, -7, -7)

D. (-82, -31, -43)

E. (10, 7, 7)

Choose the correct answer from the options given below :

A and C only

The correct answer is Option (3) → A and C only

eq. of line

$⇒\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

$⇒\frac{x-2}{8-2}=\frac{y+3}{-1+3}=\frac{z+1}{2+1}=λ$

$⇒x=6λ+2,y=2λ-3,z=3λ-1$

distance of this point from (A)

$(6λ+2-2)^2+(2λ-3+3)^2+(3λ-1+1)^2=14^2$

$36λ^2+4λ^2+9λ^2=14^2$

$49λ^2=14^2$

$λ^2=2^2⇒λ=±2$

so $P(x,y,z)$

(14, 1, 5) at x = 2 or (-10, -7, -7) at x = -2