# Product of Four Vectors JEE Notes | EduRev

## JEE : Product of Four Vectors JEE Notes | EduRev

The document Product of Four Vectors JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Product of Four Vectors

(a) Scalar Product of Four Vectors: The products already considered are usually sufficient for practical applications. But we occasionally meet with products of four vectors of the following types. Consider the scalar product of This is a number easily expressible in terms of the scalar products of the individual vectors. For, in virtue of the fact that in a scalar triple product the dot and cross may be interchanged, we may write Writing this result in the form of a determinant,

we have (b) Vector Product of Four Vectors:

Consider next the vector product of This is a vector at right angles to and therefore coplanar with Similarly it is coplanar with It must therefore be parallel to the line of intersection of a plane parallel to with another parallel to To express the product in in terms of regard it as the vector triple product of and   Similarly, regarding it as the vector product of we may write it  Equating these two expressions we have a relation between the four vectors  ...(3)

Ex.26 Show that , Sol. Ex.27 Show that So

l. K. VECTOR EQUATIONS

Ex.28 Solve the equation Sol. From the vector product of each member with a, and obtain  Ex.29 Solve the simultaneous equations Sol. Multiply the first vectorially by which is of the same form as the equation in the preceding example.

Thus Substitution of this value in the first equation gives Ex.30 Sol. Multiply scalarly by     Ex.31 If then prove that Sol.  ...(1)   Solving (2) and simultaneously we get the desired result.

Ex.32 Solve the vector equation in Sol.

Taking dot with a = ...(1)

Taking cross with a = ...(2)  Ex.33 Express a vector as a linear combination of a vector and another perpendicular to A and coplanar with and .

Sol. is a vector perpendicular to and coplanar with and .

Hence let, ...(1)

taking dot with  again taking cross with     Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

## Mathematics (Maths) Class 12

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