Respuesta :
The scalar product or dot product of the two perpendicular vectors is zero. Then the positional vector is shown below.
[tex]v_1 = \pm 8 \times \dfrac{y}{\sqrt{x^2+y^2}}[/tex]
What is a vector?
The quantity which has magnitude, direction, and follows the law of vector addition is called a vector.
Rite a formula for a two-dimensional vector field that has all vectors of length 8 and perpendicular to the position vector at that point.
Let the vector u with the position (x, y).
[tex]\rm \overrightarrow{u} = x \hat{i}+ y \hat{j}\\\\\overrightarrow{v} = v_1 \hat{i}+ v_2 \hat{j}[/tex]
The magnitude of the vector will be given as
[tex]\rm \sqrt{v^2_1 + v^2_2} = 8\\\\v^2_1 \ +\ v_2^2\ = 64[/tex]...1
We know that the dot product of the two perpendicular vectors is zero.
[tex]\rm \overrightarrow{u} \cdot \overrightarrow{v} = 0[/tex]
Then we have
[tex]\rm xv_1 + yv_2 = 0\\\\v_2 = \dfrac{x}{y}v_1[/tex]
Put in equation 1, we have
[tex]\rm v^2_1 + \dfrac{x^2}{y^2}v_1^2 = 64\\\\\\v_1 ^2 = \dfrac{y^2}{x^2+y^2} * 64\\\\\\v_1 = \pm 8 \times \dfrac{y}{\sqrt{x^2+y^2}}[/tex]
More about the vector link is given below.
https://brainly.com/question/13188123
