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WEEK FOUR
VECTORS IN THREE DIMENSIONS
CONTENTS
(a) Scalars Product of Vectors in Three Dimensions
(b) Application of Scalar Product
SUB TOPIC: SCALAR PRODUCT OF VECTORS IN THREE DIMENSIONS
The scalar product of three vectors a,b and c is defined as a.(bxc) which is a scalar quantity.
If three vectors a,b and c are given as:
a = a1i + a2j + a3k
b = b1i + b2j + b3k
c = c1i + c2j + c3k
The scalar product is found the same way as the determinant of a 3×3 matrix.
We denote dot or scalar product of two vectors A and B by A.B. This dot product is defined as the product of the magnitudes of A and B and the cosine of the angle between them.
A.B =
Scalar product otherwise called dot product (or inner products).
The Scalar product between two perpendicular vectors is zero.
Summary of the scalar product of unit vectors is provided below:
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