Find the angle between each of the following pairs of vectors a⃗ =axi^+ayj^ and b⃗ =bxi^+byj^.

Asked by maham237 @ in Mathematics viewed by 348 People

Find the angle between each of the following pairs of vectors A⃗ =Axi^+Ayj^ and B⃗ =Bxi^+Byj^.. Ax1= -3.20, Ay1= 4.40; Bx1= 2.70, By1= -3.10. i know this is dot prodoct but the calculater just keep saying error

Answered by maham237 @


The product point of the two vectors is given by:

A.B = (-3.20i + 4.40j). (2.70i - 3.10j)

A.B = (-3.20 * 2.70) + (4.40 * (- 3.10))

A.B = -8.64 -13.64

A.B = -22.28

Then, the module of both vectors is:

For vector A:

A = \sqrt{(- 3.20) ^ 2 + (4.40) ^ 2}

A = 5.44

For vector B:

B = \sqrt{(2.70) ^ 2 + (- 3.10) ^ 2}

B = 4.11

Finally the angle between the vectors is given by:

\alpha =Cos^{-1}(\frac{A.B}{|A||B|})

Substituting values:

\alpha =Cos^{-1}(\frac{-22.28}{|5.44||4.11|})

\alpha = 175

Answer:

The angle between the vectors is:

\alpha = 175


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