Question

foot of the perpendicular from (3 4 5 ) on the plane 3x+4y+5z-3=0​

Answer 1

Step-by-step explanation:

Clearly direction ratios of perpendicular drawn from origin to the given plane are 3,4,−6.

Hence, equation of perpendicular line to the given plane and passing through origin is given by,

3

x

=

4

y

=

−6

z

=k (say)

Now let foot of perpendicular be P(3k,4k,−6k)

Also this point lie in the given plane

⇒3(3k)+4(4k)−6(−6k)+1=0

⇒k=−

61

1

Hence, P≡(−

61

3

,−

61

4

,

61

6

)