angle between A-B and A×B?
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Answer:
Given,
Two vectors A and B.
A and B are two vectors. So, their sum A+B lies in the same plane where A and B lie (Since they are non -parallel so they define a plane and the cross product between them is not zero.)
A×B=∣A∣∣B∣sinαn, where α is the angle between A & B and n is the unit vector perpendicular to the plane containing A & B. So, the angle between (A+B) and (A×B) is 90
0
.
Mathematically,
∣A+B∣∣A×B∣cosα=(A+B).(A×B)
=A.(A×B)+B.(A×B)
=B.(A×A)+A.(B×B)
=0+0
Explanation:
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