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frutty [35]
3 years ago
13

George determines the mass of his evaporating dish to be 3.375 g. He adds a solid sample to the evaporating dish, and the mass o

f them combined is 26.719 g. What must be the mass of his solid sample
Physics
1 answer:
zhannawk [14.2K]3 years ago
3 0

Explanation:

The given data is as follows.

       Mass of evaporating dish = 3.375 g

    Total mass = Mass of solid sample + evaporating dish

That is, Mass of solid sample + evaporating dish = 26.719 g

Therefore, we will calculate the mass of solid sample as follows.

    Mass of solid sample = (Mass of solid sample + evaporating dish) - mass of evaporating dish

                            = 26.719 g – 3.375 g

                            = 23.344 g

Thus, we can conclude that mass of his solid sample must be 23.344 g.

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vector a = 3i - 2j - k and vector b = i + 4j + k, the unit vector, n, normal to the plane is (7i - j + 7k)/3√11

What is a vector?

A vector is a quantity having direction as well as magnitude.

Vectors can especially be used in determining the position of one point in space relative to another.

From the question,

The normal vector to the plane is c = a × b

we have that, a = 3i - 2j - k and b = i + 4j + k,

c = a × b

c = (3i - 2j - k) × (i + 4j + k)

= 3i × i + (- 2j) × i + (-k) × i + 3i × 4j + (- 2j) × 4j + (-k) × 4j + 3i × k + (- 2j) × k + (-k) × k

= 3i × i - 2j × i - k × i + 12i × j - 8j × j - 4k × 4j + 3i × k - 2j × k - k × k

It is known that

i × i = 0,

j × j = 0 and

k × k = 0.

we also have that

c = 3(0) - 2(-k) - (-j) + 12k - 8(0) - 16(-i) + 3(-j) - 2i - 0

c = 0 + 2k + j + 12k - 0 + 16i - 3j - 2i

c = 16i - 2i + j - 3j + 2k + 12k

c = 14i -2j + 14k

The unit vector normal to the plane n = c/ |c|

where |c| is the magnitude of c

= √(14² + (-2)² + 14²) = √(196 + 4 + 196)

= √396

= √(36 × 11)

= 6√11

we can write that n = c/|c|

= (14i -2j + 14k)/6√11

we simplify further

= 2(7i - j + 7k)/6√11

= (7i - j + 7k)/3√11

So, the unit vector normal to the plane is (7i - j + 7k)/3√11

Learn more about vectors at: brainly.com/question/25705666

#SPJ1

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