This IIT JEE Maths lecture discusses the scalar triple product of vectors.
While solving, the last two rows are interchanged with each other as seen in the video, and as known from the properties of determinants the answer becomes the negative of the original (initial answer was [a b c]). Then if the first and the new second line are again exchanged, the answer once again becomes [a b c] which can be written as [c a b] (all the terms used here are vectors, you would have seen a bar sign on the terms in the video). Its vector representation is now seen. With the help of a diagram showing clockwise and anti-clockwise directions of the vectors the concept of scalar triple product becomes clearer.
After this its geometrical properties are discussed. According to the first property, if any two of the three vectors are parallel or equal, the box product (scalar triple product) would be 0. Another property discussed here is that if any of the three vectors is a null vector, the value of the scalar triple product would be 0 as well.
The proof for the properties is given as well. These properties find application in solving many complicated problems. Use IIT JEE sample papers and AIEEE sample papers to practice enough problems. ‘Vectors’ is important and must never be neglected during exam preparation. This would assist you greatly while writing the actual IIT JEE papers and AIEEE papers. During the last lap of preparation never forget to practice ample questions using previous years papers (old IIT JEE question papers and other examination papers).
‘Vectors’ is one of the most important fundamental concepts for engineering entrance exams because not only does it find utility in Mathematics, but Physics as well. This is because many quantities in Physics are represented in the form of vectors (quantities involving both magnitude and direction), thus to solve questions involving qualities such as this (example: velocity, displacement etc.) one has to be thorough with the concepts of vectors.
Vectors were invented because most real-life problems include two and three dimensions (which cannot be solved using Arithmetic and the use of Geometry can be a little tiring). It is wise to practice sufficient problems from this using sample test papers and previous years papers for proper understanding.
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