contestada

70 POINTSS!!!! URGETT PLS HELP!! Vectors t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j are given.

Part A: Find the angle between vectors t and u. Show all necessary calculations. (5 points)

Part B: Choose a value for c, such that c > 1. Find w = cv. Show all necessary work. (2 points)

Part C: Use the dot product to determine if t and w are parallel, orthogonal, or neither. Justify your answer. (3 points)

Respuesta :

The angle between the vectors t and u is 45°. And the vector t and vector w are orthogonal to each other.

What is a vector?

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

The vectors are given below.

t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j

Part A: Then the angle between vectors t and u will be

[tex]\cos \theta = \dfrac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{a}| + |\overrightarrow{b}|}[/tex]

Then we have

cos θ = [(−5i + 2j)(−3i + 7j)] / [√{(-5²) + 2²} + √{(-3)² + 7²}]

cos θ = 1 / √2

      θ = 45°

Part B: c is a scalar

If [tex]\rm \overrightarrow{\rm v} = (a, b)[/tex], then [tex]\rm c\overrightarrow{\rm v} = c(ca, cb)[/tex]

Let c = 2, then we have

[tex]\overrightarrow{\rm w} = c\overrightarrow{v}\\\\\overrightarrow{\rm w} = (2*8, 2*20)\\\\\overrightarrow{\rm w} = (16, 40)[/tex]

Part C: Use the dot product to determine if t and w are parallel or orthogonal.

[tex]\overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = (-5, 2)(16, 40)\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = -5*16+ 2*40\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = -80+ 80\\\\ \overrightarrow{\rm t} \cdot \overrightarrow{\rm w} = 0[/tex]

More about the vector link is given below.

https://brainly.com/question/13188123

#SPJ1

Otras preguntas