Question

A perpendicular is drawn from the point p(2,4,-1) to the line

Answer 1

Answer:

Step-by-step explanation:

The equation of the given line is :x+51 = y+34 = z−6−9 = k (say) ....(1)The coordinates of any general point on this line are :(k−5, 4k−3, 6−9k)Let N be the foot of the ⊥ drawn from P(2,4,−1) on the line (1).Then coordinates of N are N(k−5, 4k−3, 6−9k).Direction ratios of PN are :a1 = k−5−2 = k−7b1 = 4k−3−4 = 4k−7c1 = 6−9k+1 = −9k+7Now, Direction ratios of given line (1) are : <1,4,−9>≡<a2,b2,c2>Since, PN ⊥ line (1), thena1a2 + b1b2 + c1c2 = 0⇒(k−7) + 4(4k−7)−9(−9k+7) = 0⇒k−7+16k−28+81k−63 = 0⇒98k = 98⇒k = 1So, coordinates of foot of ⊥ are N(−4, 1,−3).Now, equation of PN is : x − 2−4−2 = y−41−4 = z−(−1)−3−(−1)⇒x−2−6 = y−4−3 = z+1−2