$MathMaster logo$

MathMaster

Home
general
what is the angle between the vectors a 3i 3j 3k b 2i 1j 3k

Question

What is the angle between the vectors A= 3i + 3j + 3k B= 2i + 1j + 3k

278

likes

1389 views

Answer to a math question What is the angle between the vectors A= 3i + 3j + 3k B= 2i + 1j + 3k

$Expert avatar$

4.5

105 Answers

A=3i+3j+3k

B=2i+1j+3k

A\cdot B=\esquerda(3\vezes2\direita)+\esquerda(3\vezes1\direita)+\esquerda(3\vezes3\direita)=6+3+9=18

\esquerda|A\direita|=\sqrt{3^2+3^2+3^2}=\sqrt{9+9+9}=\sqrt{27}=3\sqrt{3}

\esquerda|B\direita|=\sqrt{2^2+1^2+3^2}=\sqrt{4+1+9}=\sqrt{14}

Deixe,\:o\:ângulo\:entre\:dois\:vetores=\theta

\cos\theta=\frac{A\cdot B}{\left|A\right|\left|B\right|}=\frac{18}{3\sqrt{3}\times\sqrt{14 }}=\frac{\sqrt{42}}{7}

\theta=\cos^{-1}\left(\frac{\sqrt{42}}{7}\right)=22,21^{\circ}

Ângulo\:entre\:dois\:vetores\:=22,21^{\circ}

Frequently asked questions (FAQs)

Math question: Find the value of c if the constant function f(x) = c remains the same for all values of x.

+

What is the value of the angle measured in radians for a point on the unit circle at (1, 0)?

+

Math question: "What is the vertex of the quadratic function y = 3x^2 + 2x + 4?"

+

New questions in Mathematics

Pedro bought 9 kg of sugar at the price of R$1.80 per kilogram, six packets of coffee at the price of R$3.90 per packet and 8 kg of rice at the price of R$2.70 per kilogram. Knowing that he paid for the purchases with a R$100.00 bill, how much change did he receive?

431414-1*(11111-1)-4*(5*3)

I need .23 turned into a fraction

The graph of the equation x²= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F(_,_) and a directrix y=_____

The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly

what is the annual rate on $525 at 0.046% per day for 3 months?

A company that manufactures personal hygiene items purchases machinery for $220,000 that is considered to last 7 years; it is estimated that at the end of the period it will have a salvage value of $1000. Find: to. The depreciation rate. b. The book value at the end of the sixth year.

Find 2 numbers whose sum is 47 and whose subtraction is 13

The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one

Estimate the quotient for 3.24 ÷ 82

Convert 9/13 to a percent

John he’s going to the carnival with his friends. He spends $25 on an admission ticket. He buys 10 games at X dollars each and two boxes of popcorn at Y dollars each. Write an expression to show the total cost of admission game, tickets and popcorn.

9.25=2pi r solve for r

Find the vertex F(x)=x^2-10x

Perform operations with the polynomials P(x) = x3 and Q(x) = 2x2 + x – 3x3 : a) P(x) - Q(x)