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

All you need of JEE at this link: JEE

**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!