Ex 11.2, 4

Transcript

Ex 11.2, 4 Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3 𝑖﷯ + 2 𝑗﷯ – 2 𝑘﷯ . Equation of a line passing through a point with position vector 𝑎﷯ , and parallel to a vector 𝑏﷯ is 𝑟﷯ = 𝑎﷯ + 𝜆 𝑏﷯ Since line passes through (1, 2, 3) 𝑎﷯ = 1 𝑖﷯ + 2 𝑗﷯ + 3 𝑘﷯ Since line is parallel to 3 𝑖﷯ + 2 𝑗﷯ − 2 𝑘﷯ 𝑏﷯ = 3 𝑖﷯ + 2 𝑗﷯ − 2 𝑘﷯ Equation of line 𝑟﷯ = 𝑎﷯ + 𝜆 𝑏﷯ 𝒓﷯ = ( 𝒊﷯ + 2 𝒋﷯ + 3 𝒌﷯) + 𝜆 (3 𝒊﷯ + 2 𝒋﷯ − 2 𝒌﷯)