Question

Find the angle between 4i−6j and −i 5j. (round to the nearest tenth of a degree if necessary. ) The angle between the vectors is?

Answer 1

If the vectors are 4i-6j and -i-5j then the angle between both the vectors is approximately 45°.

Given two vectors be  4i-6j and -i-5j.

We are required to find the angle between vectors  4i-6j and -i-5j.

A vector is basically an equation involving a linear combination of vctors with possibly unkown coefficients. Vector is basically a quantity that has both magnitude and direction but not possition.

Angle is basically measure of inclination of something with the surface.

The angles between two vectors can be find out by the following formula:

cos Θ=[dot product of both the vectors/(product of magnitude of both the vectors)

cos Θ=[4*(-1)+(-6)*(-5)]/$\sqrt{4^{2} +(-6)^{2} } *\sqrt{(-1)^{2} +(-5)^{2} }$

cos Θ=(-4+30)/$\sqrt{52}\sqrt{26}$

cos Θ=26/$\sqrt{1352}$

cos Θ=26/26.77

cos Θ=0.7070

Θ=$cos^{-1}$(0.707)

Θ=45.008

Approximately 45°.

Hence if the vectors are 4i-6j and -i-5j then the angle between both the vectors is approximately 45°.

Learn more about vectors at brainly.com/question/25705666

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