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Properties of Dot Product
u→ • (v→ + w→) = u→ • v→ + u→ • w→ (cv→) • w→ = v→ •(cw→) = c (v→•w→)
v→ • w→ = w→ • v→ v→ • 0→ = 0
v→ • v→ = ||v→||2 if v→•v→ = 0 then v→ = 0→
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Metallic spheres of radii 6 centimetre, 8 centimetre and 10 centimetres respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
41x + 53y = 135, 53x +41y =147 Ans: 41x + 53 y = 135, 53 x + 41 y = 147 Add the two equations : Solve it, to get ... x + y = 3 -------(1) Subtract : Solve it , to
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Example of Implicit differentiation So, now it's time to do our first problem where implicit differentiation is required, unlike the first example where we could actually avoid
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