Let P(3,2,6) be point in the space and Q be a point on the line r=(i-j+2k)+const(-3i+j+5k), then find the value of const for which the vector PQ is parallel to the plane x-4y+3z=1.
thank you

Question

Let P(3,2,6) be point in the space and Q be a point on the line
r=(i-j+2k)+const(-3i+j+5k), then find the value of const for which
the vector PQ is parallel to the plane x-4y+3z=1
thank you

Ajanta Trivedi · Accepted Answer

the coordinates of P are (3,2,6)
the coordinates of any point lying on the given line
r=(i-j+2k)+λ(-3i+j+5k) where  λ is a constanti
e  r=(1-3λ) i+(-1+λ) j+(2+5λ)
kcoordinates of Q are given by: ( 1-3λ , -1+λ , 2+5λ )therefore DR's of PQ are( 1-3λ-3 , -1+λ-2 , 2+5λ-6) i
e
 (-2-3λ , -3+λ , -4+5λ)since PQ is parallel to the plane x-4y+3z=1 
(1)the DR's of the line which is perpendicular to plane (1) is ( 1, -4, 3)therefore 1*(-2-3λ)-4*(-3+λ)+3*(-4+5λ)=0-2-3λ+12-4λ-12+15λ=08λ-2=08λ=2⇒λ=28=14

hope this helps you

Let P(3,2,6) be point in the space and Q be a point on the line r=(i-j+2k)+const(-3i+j+5k), then find the value of const for which the vector PQ is parallel to the plane x-4y+3z=1.thank you

Let P(3,2,6) be point in the space and Q be a point on the line r=(i-j+2k)+const(-3i+j+5k), then find the value of const for which the vector PQ is parallel to the plane x-4y+3z=1.
thank you