Question

Find the foot of the perpendicular from the point (0, 2, 3) on the line $\frac{x+3}{5}= \frac{y-1}{2}= \frac{z+4}{3}$
Also, find the length of the perpendicular.

Answer 1

Answer:

√21 units

Step-by-step explanation:

Given Find the foot of the perpendicular from the point (0, 2, 3) on the line ,\frac{x+3}{5}= \frac{y-1}{2}= \frac{z+4}{3},  

Also, find the length of the perpendicular.

 Given x + 3 / 5 = y – 1/2  = z + 4 / 3 = K, So K is a scalar vector.

Now to write the direction ratios.

So x = 5 K – 3, y = 2 K + 1, z = 3 K – 4

Let the foot of the perpendicular be x, y, z and given point is 0, 2, 3  

When the line is zero we have

5 (5 K – 3) + 2 (2 K + 1) + 3 (3 K – 7) = 0

25 K – 15 + 4 K + 2 + 9 K – 21 = 0

38 K = 38

  K = 1

Now when K = 1

X = 5(1) – 3 = 2

Y = 2(1) + 1 = 3

Z = 3(1) – 4 = - 1

Now the foot of the perpendicular is (2, 3, - 1)

Also we get √(2 - 0)^2 + (3 - 2)^2 + (- 1 - 3)^2 = √21 units

So the length of the perpendicular is √21 units

Answer 2

Answer:

Foot of perpendicular is

(2,3,-1)

Length is

$\Huge {\sqrt{21} \: \: units}$

Step-by-step explanation:

SEE THE ATTACHMENTS.