Vector A points 48° counterclockwise from the x axis.Vector B is twice as long a

Question

Vector A points 48° counterclockwise from the x axis.Vector B is twice as long as A. Their product
A × B has length A2 and points in thenegative z direction. What is the direction of vector B?(Measure from the positive x axis with thecounterclockwise direction positive.) B > 0    ????° B < 0    ????° Vector A points 48° counterclockwise from the x axis.Vector B is twice as long as A. Their product
A × B has length A2 and points in thenegative z direction. What is the direction of vector B?(Measure from the positive x axis with thecounterclockwise direction positive.) B > 0    ????° B < 0    ????° B > 0    ????° B < 0    ????°

Explanation / Answer

The magnitude or length of A x B is given by: A x B = ABsin if the length of A x B is A2 then, A2 = ABsin A = Bsin and since B is twice the length of A we have: B = 2A A = 2Asin 1 = 2sin 1/2 = sin sin = 1/2 occurs only when the angle BETWEEN the two vectorsis 1/2 which would occur when = 30 and = 150. Given the location of vector A, if the angle between the vectors is30 degrees, then vector B is above the x axis. And if the anglebetween the vectors is 150 degrees, vector B is below the xaxis. So, B > 0 would be when the angle betweenthe vectors is 30 degrees, and B < 0 iswhen the angle between the vectors is 150 degrees. B > 0 is A -30° B < 0 is A -150°

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