1. True or False: Circle your choice. Give a short explanation or show work. a. 27 - 3j is parallel to 4ï + 6k b. Let v = 4i-j + 3k, w=i-j-5k. Then - W = -10 c.i+j+ k is a unit vector T T T F F F

Q: 23. Evaluate (x8(x² - 2x - 3)dx A)1 BIO C)-I D12 E)-2 24. For a constant vector E, find the constant…

A: Let us solve above problem.

Q: a = 3i - j - 4k, b = 2i +4j - 2k, c = -i +6k a. 4a - b b. b * (c - a) c. ||a * b|| d. the angle…

A: Solution : Given, a=3i-j-4k b=2i+4j-2k c=-i+6k a.) 4a-b=4(3i-j-4k)+2i+4j-2k =14i-18k b.)…

Q: 43. Explain the differences between vectors and scalars. Provide an example of each. 44. Copy the…

A:

Q: 13. Given the points A(3,5) and B(- 3, - 7), find a. the vector equation of the line. b. the…

A: Here, the given points are A(3,5) & B(-3,-7)

Q: A large mixing tank initially contains 1000 gallons of water in which 40 pounds of salt have been…

A: Given that, the tank initially contains 1000 gallons of water with 40 pounds salt dissolved in it.…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: THE ANSWER IS IN THE EXPLANATION PART.FEEL FREE TO ASK ANY OF YOUR DOUBTS AND COMMENT IF YOU FACE…

Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

A:

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: 9. Let b, and b, be any real numbers with | b, |31 and | by151. Let u- VI - bịi + b, Vĩ – bị j +…

A: Consider the given vector: Here the objective is to prove that the given vector is a unit vector.

Q: d. Find an equation (in point-normal form) of the plane containing the points K, M and N Let R be…

A: This is a question from analytical geometry, 3D geometry, and vector algebra.

Q: Find the angle between the vectors and .

A:

Q: Find a vector that has the same direction as [4, 2,5] but has length 35.

A:

Q: Which of the following pairs of vectors are perpendicular? -/2 > and O A | -12 > and OB. - 2/2 >…

A: We need to find the pair of vectors which are perpendicular. This can be done as follows:

Q: 2. o PQRSTU is a regular hexagon. Let PO = u and RS = v. Express vector TS in terms of u and v.…

A: Given that,In vectors, two vectors are said to be equal if their magnitude are equal and their…

Q: 2. Given a vector v with initial point P₁ = (2,-5) and terminal point P₂ = (-4, 3), write the vector…

A: Disclaimer:  Since you have asked multiple questions, we will solve the first question for you. If…

Q: When - - [B] - [12] u= V then the vectors in Span{u, v} lie on a line through the origin. True or…

A:

Q: Let v = (5,1,-2) and w =(4,-4,3). Calculate v w.

A: Given,v=5i+j-2kw=4i-4j+3kWe know that if (a1i+b1j+c1k).(…

Q: Q6:- A/ Show that the vectors A. (BxC) B.(CxÃ)=C.(AxB), if the vectors A= 31-j+2k B=21+j-k C= i-…

A:

Q: Let L be the line 8x + 2 in R?. Find vectors a and b so that v a + tb with t ER is also a correct…

A:

Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: 4. Show that a 6 a + %3D

A: Here simply open the squre term and then simplify as a.b=b.a

Q: The national government procured a total of 1550 test kits for the five regions in the country. If…

A:

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Write parametric equations of the line L through the point P: (2, 0, -3) and parallel to the vector…

A:

Q: 2. Express the following vectors in rectangular coordinates: a- A rho sin(phi)a_rho+rho…

A: Base vectors for cylindrical co-ordinates are:Base vectors for spherical co-ordinates are:

Q: 5. In each case, find the x- and y-components of vector : (a) ā = 3.20 + 6.50j; = (b) Â =18.2j…

A: Given that the vectors a  A→=3.20i^+6.50j^b  A→=18.2j^-7.91i^c  A→=-12.0i^+21.2j^d  A→=5.0B→  where…

Q: Let v vector=[−4 −6] and b vector =[8 1 2] (check the image for reference) Is b vector in the…

A:

Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

A: Given- A=(1,2,0) , B=(3,4,-1), C=(4,5,2) To find the exact value of distance between point C and the…

Q: Describe the graph of the equation. r = (6 – 21) i+ 10rj O It is a line in 2-space through the point…

A: Solution :-

Q: List five vectors in Span {V₁, V₂}. Do not make a sketch. 6 - -8 HO 5 V2 7 - 9 0 II 5

A: Given vectors are: v1=65-9,       v2=-870 We have to list five vectors in Span{v1,v2}.

Q: 5. Drop a vector from the set A {sin'x,-1,1, sin 5x} to make it independent in F(-00, 00)

A: A set is linearly independent if no vector can be written as linear combination of others.