Question

What is the distance of the point ( p, q, r ) from x - axis ?

Answer 1

First- One can easily say that its y and z component will decide what is perpendicular distance, because when we say distance from x-axis of point (p,q,r) we say distance from its foot perpendicular point on x-axis and point

foot of perpendicular will be (p,0,0) and when we apply distance formula

(p−p)2+(q−0)2+(r−0)2−−−−−−−−−−−−−−−−−−−−−−−√2

it will q2+r2−−−−−−√2

second- if you know vector you can say x axis = 1i

and position vector of (p,q,r)= pi+qj+rk(A say)

and distance will be |ixA|=

we know in vector product ixi=jxj=kxk=0and ixj=k jxk=i, ixk=j

|ixA|=|oi+rj+qk|=q2+r2−−−−−−√2

Answer 2

We say distance from its foot perpendicular point on x-axis and point

Foot of perpendicular will be (p,0,0) and when we apply distance formula

(p−p)2+(q−0)2+(r−0)2−−−−−−−−−−−−−−−−−−−−−−−√2

It will be q2+r2−−−−−−√2

Second- if you know vector you can say x axis = 1i

And position vector of (p,q,r)= pi+qj+rk(A say)

And distance will be |ixA|=

We know in vector product ixi=jxj=kxk=0and ixj=k jxk=i, ixk=j

|ixA|=|oi+rj+qk|=q2+r2−−−−−−√2

                          ONE MORE ALTERNATIVE

(p-p)² + (q-0)² + ( r-0)²)½ = (q² + r²)½