Question

let a=i+j+k and b=2i+3j+k.
(i) The projection vector of b on a and its magnitude.
(ii) The vector components of b in the direction a and perpendicular to that of a.​

Answer 1

Given info : there are two vectors ; a = i + j + k and b = 2i + 3j + k

To find :

1. The projection vector of b on a and its magnitude.
2. The vector components of b in the direction of a and perpendicular to that of a.

solution : projection vector of b on a = (a.b)/|a|² (a)

= (i + j + k).(2i + 3j + k)/|√(1² + 1² + 1²)|² (i + j + k)

= (2 + 3 + 1)/3 × (i + j + k)

= 2(i + j + k)

now magnitude of projection vector = 2√(1² + 1² + 1²) = 2√3 unit

vector component of b in the direction of a = (a.b)/|a|² (a) = 2(i + j + k)

[ see projection vector of b on a]

before component of b in the direction of a = b - (a.b)/|a|² (a)

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

= 0i + j - k

Answer 2

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