Question

The equation of the line passing through origin with direction angles 2π/3 ,π/4 ,π/3 is ......,Select the correct option from the given options.
(a) x= y/-√2=z
(b) x/-1 = y/-√2=z
(c) x= y/-√2=-z
(d) x=y/√2=z

Answer 1

for solution refer attachment option c is correct

Answer 2

if direction angles are given $\alpha,\beta,\gamma$ , direction cosine will be $cos\alpha,cos\beta,cos\gamma$

Given, direction angles : 2π/3, π/4 and π/3
so, direction cosine : cos2π/3, cosπ/4 , cosπ/3
or, -1/2, 1/√2 , 1/2
or, -1/2 ,√2/2 , 1/2
hence, direction ratios : -1 , √2 , 1

so, the equation of lines passing through origin with direction ratios -1, √2 , 1 is ...
(x - 0)/-1 = (y - 0)/√2 = (z - 0)/1
or, x/-1 = y/√2 = z/1
or, x/1 = y/-√2 = z/-1

hence, option (c) is correct.