The position vector of P and Q is P = ( 6 i -3j +9k ) , Q = ( 3i -6 j -3k) , the coordinates of R is ( 5 , -4 , 2)
What is a vector ?
A vector is an object with both mass and magnitude.
It is given that
The coordinates of
P (6, -3,9 ) and Q (3, -6, -3)
point R divides line PQ internally in the ratio 1:2.
The position vectors of P, Q and R is given by p, q and r respectively.
The position vector of P and Q in terms of i, j, k is is
P = ( 6 i -3j +9k ) , Q = ( 3i -6 j -3k)
The magnitude of P = [tex]\rm \sqrt { 6 ^2 + (-3)^2 + 9^2\\[/tex]
|p| = 11.224
The magnitude of Q = [tex]\rm \sqrt { 3^2 + (-6)^2 + ( -3)^2[/tex]
|q| = 7.348
The coordinate of R is
if a point (x,y,z) divides the line joining the points (x₁,y₁) ) and (x₂ ,y₂) in the ratio m:n, then
( x, y, z ) = [tex]\rm \dfrac{ mx_2 + nx_1}{m + n} , \dfrac{ my_2 + ny_1}{m + n} , \dfrac{ mz_2 + nz_1}{m + n}[/tex]
The m : n = 1 : 2
(x,y,z) = [tex]\rm \dfrac{ 3 + 2*6}{3} , \dfrac{ (-6) + 2*(-3)}{3} , \dfrac{ (-3) + 2*9}{3}[/tex]
(x,y,z) = 5 , -4 , 2
Therefore the coordinates of R is ( 5 , -4 , 2)
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