Question

Find the Co-ordinates of the point on the line `vecr=-vecj+3veck+lambda(2hati-2hatj+hatk)` such that the sum of co-ordinates is 3.

Answer 1

`vecr=-vecj+3veck+lambda(2hati-2hatj+hatk)`

`vecr=(2lambda)hati+(-1-2lambda)hatj+(3+lambda)hatk`

x = 2λ, y = –1, z = 3 + λ  

x + y + z = 3

(2λ) + (–1 + –2λ) + (3 + λ) = 3

(2λ – 2λ + λ) + (–1 + 3) = 3

λ + 2 = 3

λ = 1

x = 2(1) = 2

y = –1 – 2(1) = –3

z = 3 + (1) = 4

∴ The point is (2, –3, 4).