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Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Scalar Product of Vectorsa1a2 + b1b2 is called the scalar product or dot product of the two vectors a = a1i + a2j and b = b1i + b2j
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
We use the scalar product to find the angle between two vectors
Use this formula rather than the full cosine rule
Notice both vectors eminate (start) from the same point!
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Special Properties of the Scalar ProductFind the scalar product of two perpendicular vectors:
Find the scalar product of two parallel vectors:
Find the scalar product of coincident vectors (the same vector):
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Vectors are perpendicular IF and ONLY IF their scalar product is 0
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Scalar Product and the Angle between Vectors
IBSL Year 1
April 27 & 28, 2016
Homework
Chapter 12.3
12I: 2 - 5, 7 - 15
![Scalar product - Gradeup · 2017-11-30 · If i, j, k are orthonormal vectors and A = Axi + A yj + Azk then jAj 2= A x + A + A2 z. [Orthonormal vectors orthogonal unit vectors.] Scalar](https://img.dokumen.tips/doc/110x75/5f9dffb20e84f03fce123be6/scalar-product-gradeup-2017-11-30-if-i-j-k-are-orthonormal-vectors-and-a-.jpg)
