Exercise 12.10. Using Properties of Dot Product Let a = (2, −3), b = (−5, 1), c = (4, −6), find each dot product: 1) (ab) c 4) ||a|| 2) a 2b . 3) a (b+c) 5) (ac) - (b · c) 6) 3 a b

Q: 22: Answer 2 branches only 35+6 A. Find the: ¹ s² +35 B. Determine if A-91-6j-24k and B=(-15,10,40)…

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Q: c+2f -18f a+ 2d b+2e If A =d ef=2, then -18d -18e ghi a) 36 b) 72 c) 2 d) -72 e)-36

A: we have,      a+2db+2ec+2f-18d-18e-18fghi  =abc-18d-18e-18fghi+2d2e2f000000

Q: Show that

A: Given,  To prove 1  1    1a    b    c  a3      b3     c3=a-b(b-c)c-a(a+b+c)

Q: b) Heron's Formula Area = √5(5-a)(s-b)(s-c), where s = 1/(a+b+c) prove using the following steps.

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Q: - 7x - 12) is simplified?

A: here after the simplify we get the True option is A

Q: 11) y2+ 2y+ 1

A: simplify the equation

Q: 2. ) If a = 3i, b = i+j, c= i – 2j then: a) Find a + b + c in in i, j form. b) Find b + 2c in i, j…

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Q: 2) -3x + y = 23 A) (4,1) C) (-8, -1) B) (-4,-1) D) (1,4)

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Q: What is the simplest form of the product? V18x°y7 • \2x³y6

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Q: geles B=} AtC= | AtC-2D= -2 う -2D = -3 2の I +3

A: As per guidelines we can elaborate and solve your query as answer below.

Q: , y = X = t+2 t+2,

A: The solution of the problem is given in the next step.

Q: What is the inverse of the equation y-3r - 27 B) y-x C) y-' D y-2r-3 A) y-3x + 2 C

A: Consider the equation: y = 3x - 2

Q: Which of the following make sense (where all the dots denote the dot product)? Explain your answer.…

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Q: Question 10 Evaluate f - x3+27 dx. x+3 x3 A.) 3 + 9x + C x3 В.) 3x2 + 9x + C 2 C.) 3x2 + - 9x + C…

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Q: 1. If i = [2,-4, −1] and v = [1, −2, 4] find: a) 30-u c) Find G, where F(2, −3, 4) and FG = 3v b)…

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Q: 7. Approximate (22 + 3) dz using four rectangles and the left endpoint method.

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Q: Find the dot product 9) v = 12i + 9j, w = -10i – 8j

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Q: a det d e f = -4. g h i Let -2f — 2е -2d The value of det a corresponds to: 8с +i 8b +h 8a +g a) 64…

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Q: parallelogram ABCD, find BC. B 18 C 10 A1 8 [B] 10 [C] 28

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Q: B. Determine orthogonal $2435 if A=9i-6j-24k and B=(-15, 10,40) are parallel, or neither using dot…

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Q: 2x + 1 3 – 4x Consider the function y = f(x) a) find Ax + h) simplify fully Ax + h) – Ax) h b) find

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Q: Q6: Determine whether AB is parallel or perpendicular to CD whe a) A(0,-1): B(1,1) ; C(1,5) D-1,1)…

A: to check the lines are parallel or perpendicular

Q: 8) What is the value of a when y-- 2x+ is placed in the form y= a(x- h) + k? A) -3 C) 6. 1 B) 3. D)…

A: Given: y=−13x2−2x+23

Q: Need c) only use product rule 3. Differentiate. a) M(u) = (1– 4u²)(u+2) b) g(x)= (-x+ 3)(x- 10) c)…

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Q: Let å = [3,-2,1]; B = -21-1-2k; č= i+j;d36j. %3D nd (6+).d)? A) -2 C) -3 G) i + 2j - 2k B) 2 D) -1…

A: a→=3, -2, 1,  b→=-2i-j-2k,  c→=i+j Now, b→+c→=-2i-j-2k+i+j=-i-2k

Q: f 7 V√x dx 21

A: Introduction: Integration can be considered the reverse process of differentiation or called…

Q: Q2: IF A=3i+k and B=i+2j-2k Find a) 2A-B b)A.B C) BX (A x B)

A: Vector: A quantity that has both magnitude and direction is called a vector Sum and Difference of…