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If the straight line drawn through the point P 3 , 2 and inclined at an angle π 6 with the x - axis meets the line 3 x - 4 y + 8 = 0 at Q, then the length of PQ is

Correct answer

6

Step-by-step solution

Point Q can be obtained by using parametric form of a straight line, ⇒ Q ≡ 3 - 3 r 2 ,     2 - r 2 Also, point Q is on 3 x - 4 y + 8 so it will satisfy this equation, hence, 3 3 - 3 r 2 - 4  2 - r 2 + 8 = 0 3 - 3 2 r - 8 + 2 r + 8 = 0 ⇒r 2 - 3 2 = - 3   ⇒ r = - 6 Hence, the length of PQ = 6

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