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Two vectors A and B have equal magnitude and perpendicular to each other . Then the vector A + B is perpendicular to - (A)A×B (B)A-B (C)3A-3B(D)ALL OF THESE

Two vectors A and B have equal magnitude and perpendicular to each other . Then the vector A + B is perpendicular to - (A)A×B (B)A-B (C)3A-3B(D)ALL OF THESE

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
The resultant of the vectorsl,\vec{A}+\vec{B}, willl lie along the diagonal of the square formed with\vec{A}and\vec{B}as adjacent sides.\vec{A}-\vec{B}willl be along the diagonal of the square with one of the side reverse about the point of intersection of the vectors. And hence the two vectors will be perpendicular to each other. Also only the magnitude3\vec{A}-3\vec{B}is larger than that of\vec{A}-\vec{B}, but the direction is same, and so it is also perpendicular to\vec{A}+\vec{B}.
Also\vec{A}\times \vec{B}is perpendicular to the plane containing\vec{A}, \vec{B}and\vec{A}+ \vec{B}.

Hence all of these are correct answers.

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