Question

) JĀ = 4,8 = -4ſ them angle of A + B with X-axis is equal to;

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Answer 1

Answer:

hope this will help u

Explanation:

The magnitude of a vector product(or cross product) of vector [math]A[/math] and vector [math]B[/math] would be

[math]|A||B|sinø[/math]

Where [math]ø[/math] is the angle between the vectors [math]A [/math] and [math]B[/math]

Therefore, here

[math]|A||B|sinø=8[/math]

[math].: 2*5sinø=8[/math]

[math].: 10sinø=8[/math]

[math].: sinø=8/10[/math]

[math].: sinø= 4/5[/math]

Dot product of vector [math]A[/math] and vector [math]B[/math] i.e [math]A.B[/math] would be

[math]|A||B| cosø[/math]

From previous calculations , we got [math]sinø=4/5[/math]

[math]sin^2ø + cos^2ø =1 [/math](it is a trignometrical identity)

[math].: (4/5)^2 +cos^2ø =1[/math]

[math].: cos^2ø =1 - 16/25[/math]

[math].: cos^2ø=9/25[/math]

[math].: cosø=3/5(plus or minus)[/math]

Therefore the dot product [math]A.B[/math] would be

[math]|A||B|cosø[/math]

[math]= (2*5)(3/5)(plus or minus) = 10(3/5)(plus or minus) =2(3)(plus or minus) = 6(plus or minus)[/math]

Therefore the answer is [math]A.B [/math]= 6[math](plus or minus)[/math]