To find the projection of vector [tex]\((2, 6)\)[/tex] onto vector [tex]\((-1, 5)\)[/tex], we proceed through several steps:
1. Determine the Dot Product of the Vectors:
[tex]\[
\text{Dot product} = (2)(-1) + (6)(5) = -2 + 30 = 28
\][/tex]
2. Calculate the Magnitude Squared of the Second Vector:
[tex]\[
\text{Magnitude squared of } (-1, 5) = (-1)^2 + 5^2 = 1 + 25 = 26
\][/tex]
3. Compute the Projection Scalar:
[tex]\[
\text{Projection scalar} = \frac{\text{Dot product}}{\text{Magnitude squared}} = \frac{28}{26} = 1.07692307692
\][/tex]
4. Find the Projection by Multiplying the Scalar with the Second Vector:
[tex]\[
\text{Projection} = 1.07692307692 \times (-1, 5)
\][/tex]
This gives us:
[tex]\[
\text{Projection} = (1.07692307692 \cdot -1, 1.07692307692 \cdot 5) = (-1.07692308, 5.38461538)
\][/tex]
Therefore, the projection of [tex]\((2, 6)\)[/tex] onto [tex]\((-1, 5)\)[/tex] is represented by the scalar multiplying the vector [tex]\((-1, 5)\)[/tex]:
The correct answer is:
A. [tex]\(1.08(-1,5)\)[/tex]
