Analysis and Approaches for IBDP Maths Ebook 2

Your Practice Set – Analysis and Approaches for IBDP Mathematics SUMMARY POINTs � Properties of the vector product u� v of angle between u and v : �u1 � � � u � u2 and �u � � 3 � 1. �u2v3 � u3v2 � � � u� v � u ˆ 3v1 � u1v3 � u v sin�n , where nˆ //( u� v ) �u1v2 � u2v � � 1 � 2. i�i � j� j � k �k � 0 3. i�j �k , j�k �i and k �i � j 4. j�i � �k , k � j � �i and i�k � �j 5. u and v are parallel if u�v �0 6. u and v are perpendicular if u�v � u v 7. u� v � �( v�u ) �v1 � � � v � v2 where � is the �v � � 3 � � The area of the parallelogram with adjacent sides AB � and AD � is AB� AD � � � The area of the triangle with adjacent sides AB � and AD � is 1 AB� AD 2 � � � The volume of the parallelepiped formed by AB � , AD � and AF � � � � � � �AB�AD ��AF � � is � Forms of the straight line with fixed point A( a1, a2, a 3) and direction vector b � b i � b j� b k : 1. 2. 1 2 3 � x � � a1� � b1� � � � � � � y � a �t b , t � 2 2 � z � � a � � 3 b � � � � � � 3� � x �a1�b1t � �y � a2 � b2t : Parametric form � � z � a3 � b3t x �a1 y �a2 z� a3 3. � � ( � t) : Cartesian equations b b b 1 2 3 78 SE Production Limited

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