Question

Find the equation of line joining (1 ,2, 3) & (-3 , 4 , 3) and show that
it is perpendicular to z axis

Answer 1

we know that very well that equation of vector for a line passing through 2 points vector a and vector b can be given by,

vector a= (1 ,2, 3) & vector b= (-3 , 4 , 3)

total vector is denoted by R,

R=a+k(b-a)==>C

vector a= 1i+2j+3k

vector b= -3i+4j+3k

put the values of vector a and vector b in equation C

vector a=a

vector b=b

R=i+2j+3k+k(-3i+4j+3k-i-2j-3k)

R=i+2j+3k+k(-4i+2j)

R is a vector for a line passing through 2 points vector a and vector b can be given by,

R=i+2j+3k+k(-4i+2j)

now with the help of doth product,

vector called as unit vector along with z-axis is denoted by k,

direction ration is (0,0,1)

and direction line (-4 2 0)

if two lines perpendicular to each other then we know that,

=0*-4+0*2+1*0

=0

so that it is perpendicular to axis Z.