1. Scalar Product of Vectors
Notes:
- We can perform addition, subtraction and multiplication of vector quantities. However, division of them is not possible.
- During multiplication, we may get a scalar result or a vector result depending upon the type of multiplication we choose.
- There are two types of multiplication of vectors: Dot Product and Cross Product.
- In class 10, we have discussed only Dot Product and this always gives us a scalar quantity as a result.
- \vec{a}.\vec{b} = |\vec{a}|.|\vec{b}| cos \theta
Important:
- When \theta = 90°, \vec{a}.\vec{b}=0
1. Find the scalar product of given pair of vectors:
a) \vec{a} = 4\vec{i} + 6\vec{j} and \vec{b} = 6\vec{i} + 7
\vec{j}
Solution:
Here,
\vec{a} = 4\vec{i} + 6\vec{j} = (4,6)
\vec{b} = 6\vec{i} + 7 \vec{j} = (6,7)
\vec{a}.\vec{b} = (4*6+ 6*7)
= (24+42)
= 66
c) \vec{a} = 5\vec{i} + 3\vec{j} and \vec{b} = 2\vec{i} -4
\vec{j}
Solution:
Here,
\vec{a} = 5\vec{i} + 3\vec{j} = (5,3)
\vec{b} =2\vec{i} -4 \vec{j} = (2,-4)
\vec{a}.\vec{b} = 5*2+ 3*(-4)
= 10-12
= -2
e) \vec{a} = 3\vec{i} + 8\vec{j} and \vec{b} = 5\vec{i} + 12
\vec{j}
Solution:
Here,
\vec{a} = 3\vec{i} + 8\vec{j} = (3,8)
\vec{b} = 5\vec{i} + 12 \vec{j} = (5,12)
\vec{a}.\vec{b} = (3*5+ 8*12)
= (15+96)
= 111
g) \vec{a} = \left ( 6 \\ -4 \right ) and \vec{b} = \left ( -3
\\ -5 \right)
Solution:
\vec{a}.\vec{b} = \left ( 6 \\-4 \right) . \left ( -3 \\ -5
\right)
= 6(-3) + (-4)(-5)
= -18 + 20
= 2
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About this page:
Class 10 - Scalar Product of Vectors Solved Exercises | Readmore
Optional Mathematics is a collection of the solutions related
to proofs of scalar product of vectors from the vector chapter for
Nepal's Secondary Education Examination (SEE) appearing students.
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