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Given: (x₁,y₁) = A(3, 4), θ = 30°

To find:

Length PQ.

Explanation:

So, the equation of the line is

Formula Used:

⇒

⇒

⇒ x – √3 y + 4√3 – 3 = 0

Let PQ = r

Then, the coordinate of Q are given by

⇒ x , y

The coordinate of point Q is

Clearly, Q lies on the line 12x + 5y + 10 = 0

⇒

⇒ r

PQ = |r|

Hence, the length of PQ is