Duduli

Answer:- If two vectors can be represented both in magnitude and direction by the two sides of a triangle taken in the same order, then the resultant is represented completely, both in magnitude and direction, by the third side of the triangle taken in the opposite order.

Answer:- If vector is resolved into two or more vectors whose combined effect is same as that of the given vector,then the resolved vectors are called the components of the given vector.This is called resolution of vector.The resolution of a vector is opposite to that of vector addition.

Answer:- Let four points are A,B,C,D which are lies in one plane.the position vector of their with respect to origin are OA,OB,OC & OD respectively. Now,AB=OB-OA         AC=OC-OA          AD=OD-OA We know 1/6{AB•(AC×AD)} gives the volume of tetrahedron. if four vectors lies in one plane(coplanar) then their volume is zero[i.e AB•(AC×AD)=0]. So to prove the given four vectors are coplanar we have to show the determinant of AB•(AC×AD) is zero. Are you satisfied by this answer

Reason:- We know in a•(b×a),b×a vector is perpendicular to both a vector & b vector.so angle between a vector & b×a vector is 90°.(Angle,x=90°) I.e a•(b×a)=|a||b|cosx=|a||b|cos90° I.e a•(b×a)=0 ( because cos90°=0). It is the answer to the question why a•(b×a ) or b•(c×b) or c•(a×c) all are give zero value. Are you satisfied by this answer

Answer We know scalar triple product of three vectors give volume of parallelopiped.if three vector lies in one plane(i.e coplanar)then their is no volume that implies  I.e scalar triple product is zero {a•(b×c)=0} when three vector lies in one plane. Are you satisfied by this answer

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