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Theorem
a→ • b→ = ||a→|| ||b→|| cos•
Proof
Let us give a modified version of the diagram above.
The three vectors above make the triangle AOB and note that the length of each side is nothing much more than the magnitude of the vector forming that side.
The Law of Cosines defines that,
||a→- b→||2 = ||a→||2 + ||b→||2 - 2 ||a→|| || b→|| cos•
As well by using the properties of dot products we can write the left side as,
||a→- b→||2 = (a→ - b→) • (a→ - b→)
= a→• a→ - a→•b→ - b→•a→ + b→• b→
= || a→||2 - 2a→ • b→ + || b→||2
After that our original equation is,
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What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication
find inverse of [1 2 3 2 4 5 3 5 6]
The arm of a ceiling fan measures a length of 25 in. What is the area covered through the motion of the fan blades while turned on? (π = 3.14) The ceiling fan follows a circula
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In the given figure, ∠AEF=∠AFE and E is the mid-point of CA. Prove that BD/CD = BF/CE Ans: Draw CG ¦DF In ΔBDF CG ¦ DF ∴ BD/CD = BF/GF .............(1)
Let's here start thinking regarding that how to solve nonhomogeneous differential equations. A second order, linear non-homogeneous differential equation is as y′′ + p (t) y′ +
use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0
Logarithmic form and exponential form ; We'll begin with b = 0 , b ≠ 1. Then we have y= log b x is equivalent to x= b y The first one is called
a + b
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