Question

In: Math

For the following exercises, calculate u ⋅ v. Given v = 〈−3, 4〉 draw v, 2v, and 1/2 v.

For the following exercises, calculate u ⋅ v.

Given v = 〈−3, 4⟩ draw v, 2v, and 1/2 v.

Solutions

Expert Solution

Consider the vector v with the components (-3, 4)

 

Vector v starts at point (0, 0) and terminates at point (-3, 4). The graph of vector v is as follows:

 

Compute 2v by multiply each component of vector v by 2.

2v = {2 × (-3), 2 × 4}

     = (-6, 8)

 

Vector 2v starts at point (0, 0) and terminates at point (-6, 8). The graph of vector 2v is as follows:

 

Compute ½v by multiply each component of vector v by 1/2.

1/2v = 1/2(-3, 4)

         = {1/2 × (-3), 1/2 × 4}

         = (-3/2, 2)

 

Vector 1/2v starts at point (0, 0) and terminates at point (-3/2, 2). The graph is as follows:

Junaid answered 1 year ago
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