Question

Direction cosines of the line given by equations: `(2x-1)/4=(1-y)/3=(-z)/6` are ______.

Options

• 2, –3, –6

• `2/7,(-3)/7,(-6)/7`

• `2/7,(-3)/7,6/7`

• `4/sqrt61,(-3)/sqrt61,(-6)/sqrt61`

Answer 1

Direction cosines of the line given by equations: `(2x-1)/4=(1-y)/3=(-z)/6` are `bbunderline(2/7,(-3)/7,(-6)/7)`.

Explanation:

`(x-x_1)/a=(y-y_1)/b=(z-z_1)/c`

`(2x-1)/4=(1-y)/3=(-z)/6`

`(x-1/2)/2=(y-1)/-3=(z-0)/-6`

Direction ratio = (a, b, c) = (2, –3, –6)

`sqrt(a^2+b^2+c^2)=sqrt(2^2+(-3)^2+(-6)^2)`

= `sqrt(4+9+36)`

= `sqrt49`

= 7

Direction cosines = `2/7,(-3)/7,(-6)/7`