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ollegr [7]
3 years ago
15

Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k​

Mathematics
1 answer:
valkas [14]3 years ago
7 0

Answer:

\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k​, the vector projection of B unto a is expressed as proj_ab = \dfrac{b.a}{||a||^2} * a

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k  =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||²  = 130

proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\

<em>Hence the projection of b unto a is expressed as </em>\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\<em></em>

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Step-by-step explanation:

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3 years ago
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Answer:

  • \boxed{\sf{3x^3+4x^2-25x-30}}

Step-by-step explanation:

\underline{\text{SOLUTION:}}

To isolate the term of x from one side of the equation, you must multiply by a polynomial.

\underline{\text{GIVEN:}}

:\Longrightarrow: \sf{(x+3)(3x^2 - 5x - 10)}

<u>You have to solve with parentheses first.</u>

:\Longrightarrow \sf{x\cdot \:3x^2+x\left(-5x\right)+x\left(-10\right)+3\cdot \:3x^2+3\left(-5x\right)+3\left(-10\right)}

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<u>Then, rewrite the problem down.</u>

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<u>Combine like terms.</u>

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<u>Solve.</u>

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<u>Then rewrite the problem.</u>

\Longrightarrow: \boxed{\sf{3x^3+4x^2-25x-30}}

  • <u>Therefore, the correct answer is 3x³+4x²-25x-30.</u>

I hope this helps! Let me know if you have any questions.

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