Question

What is the best approximation of the projection of (5, -1) onto (2, 6)

Answer 1

Answer with explanation:

Suppose we represent ordered pairs in terms of vectors.

$\vec{A}$

Ordered pair of points , (5,-1) in terms of vectors is represented by = 5 i - j

$\vec{B}$  

Ordered pair of points , (2,6) in terms of vectors is represented by =2 i + 6 j

Projection of Vector A on Vector B

  $\frac{(\vec{A}.\vec{B})(\vec{B})}{|\vec{B}|^2}\\\\=\frac{[(5i-j).(2 i+6 j)](2 i+6 j)}{\sqrt{2^2+(6)^2}}\\\\=\frac{(10-6)(2 i+6 j)}{\sqrt{40}}\\\\=\frac{4}{6.325}\times (2i+6j)\\\\=0.6324\times (2 i+ 6j)$

= 0.6324 (2,6)        

Answer 2

Answer:

B. 0.10(2, 6)

Step-by-step explanation:

A careful graph of the vectors can help you answer this question. The end point of the projection of (5, -1) onto (2, 6) is (0.2, 0.6) = 0.10(2, 6).