Question

Find the projection of the vector 4i-3j+k on the line passing through the points (2,3,-1) (-2,-4,3)

Answer 1

We have to find the projection of the vector 4i - 3j + k on the line passing through the points (2, 3, 1), (-2, -4, 3).

Solution : to solve easily, let A = 4i - 3j + k , B = (2,3, -1) = 2i + 3j - k and C = (-2, -4, 3) = -2i - 4j + 3k

Line BC = C - B

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

= -4i - 7j + 4k

So, |BC| = √{(-4)² + (-7)² + 4²} = √(16 + 49 + 16) = √81 = 9

now projection of the vector A on BC = A.(BC)/|BC|

= (4i - 3j + k).(-4i - 7j + 4k)/9

= (-16 + 21 + 4)/9

= 1

Therefore projection of vector 4i - 3j + k on the line passing through (2, 3, -1) , (-2, -4, 3) is 1.