Question

The angle which the line `x/1 = y/-1 = z/0` makes with the positive direction of Y-axis is ______.

पर्याय

• `(5pi)/6`

• `(3pi)/4`

• `(5pi)/4`

• `(7pi)/4`

Answer 1

The angle which the line `x/1 = y/-1 = z/0` makes with the positive direction of Y-axis is `underlinebb((3pi)/4)`.

Explanation:

Given line is  `x/1 = y/-1 = z/0` 

∴ Direction ratios of line are: 1, −1, 0

We know that direction ratio of y-axis are 0, 1, 0

`cos θ = (overset->b_1  .  overset->b_2)/(|overset->b_1| . |overset->b_2 |)`

= `((hat i - hat j) . (hat j))/(sqrt((1)^2 + (-1)^2) · sqrt((1)^2))     ...[∵ overset-> b_1 = hat i - hat j and overset->b_2 = hat j]`

= `-1/sqrt2`

∴ `cosθ = cos((3pi)/4)`

⇒ `θ = (3pi)/4`