The vectors b and c are coplanar with the triple product. The cross product of vector a with the cross products of vectors b and c is known as their Vector triple product. The volume of a parallelepiped is calculated using the scalar triple product, where the three vectors indicate the parallelepiped’s neighboring sides. The box product and mixed product are other names for it. For example, if a, b and c are three vectors, the scalar triple product is a. The dot product of a vector with the cross product of two different vectors is called the scalar triple product. Difference between Scalar Triple Product and Vector Triple Product Therefore, the products are also coplanar. Prove that a x b, a x c, and b x c are also coplanar.ĪNS: As they are coplanar, we can write them as Suppose vectors a, b and c are coplanar.If it isn’t, we use the principles of cross-product to shift to the left and then use the same procedure. Only if the vector outside the bracket is on the leftmost side, does the formula r=a1+λb hold true.Vector r=a×(b×c) is coplanar to b and c and perpendicular to a.A vector triple product yields a vector quantity as a result.Where a × (b × c) ≠ (a × b) ×c Properties of Vector Triple Product Study the detailed example of this series to make yourself even more familiar with the topic. Furthermore, a geometric sequence’s behavior depends on the common ratio’s value. The formula of this series is- sum = a/(1-r), where ‘a’ is the first term while ‘r’ is the common ratio. There is no last term in this series, and its continuation will occur forever. Now, the continuation of this pattern can take place to give us the following sums in infinite geometric series:Īn infinite geometric series is the sum of a geometric sequence of an infinite nature. Now, solving further a1 + a1 r = 5 + 2.5 = 7.5 Now, the summing of the first few terms is as follows: The series will converge to some value because the common ratio for the above sequence is between -1 and 1. The common ratio in the above series shall be r = 0.5. The first term in the above series shall be a1 = 5 The below-detailed example in this infinite geometric series study material will help you get a good grasp on the topic.Ĭonsider a series: 5 + 2.5 + 1.25 + 0.625 + 0.3125…, Infinite Geometric Series Study Material Detailed Example Here, the r’s value is such that −1 < r < 1.Īn important point to note is that the common ratio is between two consecutive terms and −1 < r < 1. The infinite geometric series formula is as follows: if the value of r is such that −1 < r < 1, it can be given as, The formula is the first thing to study in the study material notes on infinite geometric series.
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