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Johathan Wehner

Feb 20, 2025

consider two vectors:A=3i-2j and B=-i-4j. calculate |A+B|; |A-B|; the direction of A+B and A-B.”?

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Alycia Zemlak

Feb 20, 2025

add (or subtract) i components with each other, and do the same for j for A+B, the resultant vector is (3-1)i+(-2-4)j = 2i-6jthe magnitude is sqrt[2^2+(-6)^2]=6.32we know the vector will lie in the fourth quadrant, so we get the direction from tan(theta)=y component of resultant/x component of resultant = -6/2=-3theta=arctan(-3)=71.6 deg or 71.6 deg below the x axis, or 288.4 deg counterclockwise up from the x axisfor A-B:we have A-B=(3-(-1))i +(-2-(-4))j = 4i+2jmagnitude =sqrt[4^2+2^2]=4.47vector is in the first quadrant; tan(theta)=2/4=1/2theta=arctan(1/2)=26.6 deg up from the x axis... Show More
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