A line lies in the xy-plane and makes an angle of 30∘ with the positive x- axis. Find its direction cosines.

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(√3 , 1 , 2)

2 2

(√3 , 3 , 0)

2 2

(√3 , 1 , 0)

2 2

(√3 , 5 , 4)2 2

answer is C.

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Detailed Solution

As we know that 𝑥 - axis and 𝑦 - axis are perpendicular to each other.
Hence, the angle which the yellow line makes with 𝑦 - axis will be complimentary. Therefore,, the angle = 90∘ − 30∘ = 60∘.
Hence, the line is making an angle of 60∘ with the 𝑦 - axis.
Now, the 𝑥𝑦 − plane will be perpendicular to the 𝑧 - axis. So, it will make an angle 90∘ with the 𝑧 − axis. Since, the direction cosines are the cosines of all the angles. So, it will be (𝑐𝑜𝑠 30∘, 𝑐𝑜𝑠 60∘, 𝑜𝑠 90∘).

By putting the values, we get,
Direction cosines are (√3 , 1 , 0).

2 2
Hence, its direction cosines is (√3 , 1 , 0).
2 2

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