The value of the c will be (0 i+0 j+0 k). c is a vector that is along the positive x-axis and has the condition a(b+c)=0.
<h3>What is a vector?</h3>
A vector is a quantity or phenomena with magnitude and direction that are independent of one another. The phrase also refers to a quantity's mathematical or geometrical representation.
Given ;
a=3i-2j+k
b=-i-4j+3k
Given property:
a(b+c)=0
-i-4j+3k ((-i-4j+3k)+c)=0
(3+8+3)(-i-4j+3k)c=0
14(-i-4j+3k)c=0
c=0 i+0 j+0 k
Hence, the value of the c will be (0 i+0 j+0 k).
To learn more about the vector refer to the link;
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Answer:
1) Mass of the string = 0.0267kg
Explanation:
1) In the above question, we are given:
Length of guitar string = 60cm
Wave speed = 30.0m/s
Tension = 50N
9.81 N = 1 kg
50N = 50/9.81
= 5.10kg
We have the formula
v = √(F/μ)
Where F = the tension in the string in newtons,
v = the wave speed in m/s
μ = the mass per unit length of the string in kg/m
The formula for μ is derived as
v = √(F/μ)
Square both sides
v² = [√(F/μ)]²
v² = F/μ
μ = F/v²
From the question,
μ = 40/ 30.0²
μ = 0.044kg/m
To calculate the mass of the string we use the formula
μ = Mt / Lt = total mass/total length.
Total length = 60cm
In meters = 0.60m
0.044kg/m = Mt/ 0.60m
Mt = 0.0266666667kg
Mass of the string = Approximately 0.0267kg
2)