Which of the followings are false? I. L, : x = 1 +t, y= -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3+ 8, z = –3+4s are skew lines. II. L1 : I+1 = and L2 : x + 3 = 8 z+3 are skew lines. 3 III. L1 : x = –6t, y = 1+ 9t, z = –3t and L2 : x = 1+2s, y = 4 – 3s, z = s are parallel lines. O a.I O b. I, II O c. I, II O d. II O e. I

Q: 1. Idenfify ail pairs of parallel a). b). F c)

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

Q: 4) Consider a particle MOu along astraight line ha s eločil funchonv=ť'+xT-15 1st=6 a) Frnd…

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Q: Express the following as linear combinations of u= (2, 1, 4), v= (1, -1, 3), and w= (3, 2, 5). (a)…

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Q: Express the following: as a linear combination of u = (2, 1, 4), v = (1, -1, 6) and w = (2, 2, 8).…

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Q: 3. There are three line segments of the following lengths: 4.5 cm, 5.5 cm, and 10cm Which statement…

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Q: 4 Given F(r, s,t) = r (7sª + 7t°), compute: Frst

A: We are given, F(r,s,t)=r(7s4+7t5)⇒F=7rs4+7rt5⇒Ft=0+7r(5)t4( Partial derivative with respect to…

Q: Given thatA = ax + Q ay + az and B = Q ax + ay + az, if A and B are normal * to each other, Q is

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Q: 40 If f (ax)=L y ifind the divideddifferonces x21 flaib), flaibic) and fla,b,c,d),

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Q: describes. A v 1.4 <r< 5 and 0 <0 < 2n ? v 2.4 <r<5 and a/2 < e< 3n/2 B ? v 3.0 <r<5 and 3/2 < 0< 2n…

A: According to figure shown below, answer all questions.

Q: 4. Find the cross product 7 x 7 given that d = (0, -4, 1) and ở = (1, 1, –2).

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Q: What is the normal line to the line that passes through (-8,0) and (-1,3) 3x-7y=-24 C (x/8) +…

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Q: Express the following as a linear combination of u = (2, 1, 3), v = (1, -1, 4) and w = (3, 2, 6).…

A:

Q: 9 At what point do the following lines in R³ intersect? h: (x, y, z)=(3, 1, 2) + s(1,0,2), SER 1₂:…

A: Let's find point of intersection.

Q: 9. If y = V-|x|, then D =

A: We can differentiating given function in the in particular domain.

Q: If|u|= 3 and|v|= 6, find|u×v|and whether u×v points into or out of the page.

A: If|u|= 3 and|v|= 6, find|u×v|and whether u×v points into or out of the page.

Q: 4. What are the values of A, B, C, and D so that 1 a. A = b. A = C. A = d. A = HALA00 B= C= B B 1 8'…

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Q: 2. A single factor experiment was performed for 4 levels of the factor with 8 replicates. It was…

A: given y1¯=15 , y2¯=11 , y3¯=13 , y4¯=18 , MSE=4 two contrast τ1=μ1-μ4τ2=μ1-μ2-μ3+μ4 explanation…

Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: is a linear combination of vi = V2 = u= ulgn Ins

A: See solution below

Q: Express the following as a linear combination of u =(3, 1, 7), v = (1, -1, 4) and w= (18, 7, 8).…

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Q: The commentary of this proof contains two mistakes: WAR 2. M → R 3. W + M .. W v R 4. W VE 1 5. M HE…

A: Consider the given proof sequence. The premises are as follows. 1. W∧R2. M→R3. W↔M The conclusion is…

Q: 23. Let A = {(x, y), 4.x² + 9y² < 36} C R? Is A connected? pathwise connected? Justify your answer.

A: We Know that connected space is a topological space that cannot be represented as the union of two…

Q: Express the following as a linear combination of u= (3, 1, 7), v = (1, -1, 7) and w = (6, 3, 6).…

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Q: What is the normal line to the line that passes through (-8 , 0) and (-1, 3) 3x-7y = - 24 O (x/8) +…

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Q: 4. In AMAP and ATIE, LA = LI and ZP = LE. a. What is the relationship between ZM and ZT? b. If mZA=…

A: Given:- In ⧍MAP and ⧍TIE,∠A = ∠I and ∠P = ∠E. To find:- a. What is the relationship between ∠M and…

Q: c ls tE line cregmentfoom (3,4,0) to | (1,4,2) computef (zty?)ds&dp

A: The curve C is the line segment from 3,4,0 to 1,4,2. The parametric equation of this curve is given…

Q: 6. Use the Side-Splitter Theorem to find z given that NQ is parallel to OP. 3 N 18 24 M 18 5 4

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Q: What is the normal line to the line that (passes through (8, 0) and (-1,3 3x - 7y = - 24 O (x/8) +…

A: We will first find the slope of the line that passes through the two given points. The slope of the…

Q: 1. A bowl contains 10 red and 10 yellow balls, how many balls must be selected to ensure 5 yellow…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

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Q: Find the angle (in DMS) between the line L1 through the points P1(2, 1, 4) and P2(–1, 4, 1) and the…

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Q: What is the normal line to the line that passes through (8 , 0) and (-1, 3) 3x - 7y = - 24 (x/8) +…

A: We are given the points: 8,0 and (-1,3) Slope of the line: 3-0-1-8=-13 Equation of line that passes…

Q: 2 Let aj 3 (a) Write b as a linear combination of a and a2.

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Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v – w + 3z = 0. z =

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Q: 2. If AWXY~AVTU find the measure of ZT. W (2r-2) (8x- 7) Y (3r - 6)

A: Given  ∆WXY~∆VTU To find ∠T

Q: What is the normal line to the line that passes through (8 , 0) and (-1, 3) 3x - 7y = - 24 O (x/8) +…

A: we have to find out the equation of normal line  given points are a(8,0)  b(-1,3) of simple equation

Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

A:

Q: Express the following as a linear combination of u = (4, 1, 6), v = (1, -1, 6) and w = (1, 6, 7).…

A: The objective is to find (7, 10,7) as linear combination of u, v, w.

Q: Express the following as a linear combination of u = (4, 1, 6), v = (1, -1, 5) and w = (4, 3, 8).…

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Q: Suppose a fair die is tossed two times. Let X be the larger of the two faces that appear. Find px…

A: Solution: From the given information, a fair die is tossed two times.

Q: 2t+9 dt (t2–14t+46) 2t + 9 2t + 9 dt (t – 7)2 – 3° J[(t – 7)2 – 3]² Option 2 Option 1 2t + 9 dt [(t…

A: Here, to rewrite the given integral: ∫2t+9(t2-14t+46)52dt...(1)

Q: Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4…

A: Given Information: No. of red balls = 3 No. of blue balls = 4 No. of white balls = 5 X : number of…

Q: 15. In AXYZ, if ZX = Z , XY = 13r - 21, YZ = 8r – 6, and XZ = x + 4, find x and the measure of each…

A: Solve 15

Q: Express the following as a linear combination of u= (4, 1, 6), v = (1, -1, 5) and w = (1,3,7). (10,…

A: We need to express as linear vector.

Q: Check That

A: Given: ∂2W∂U∂T=∂2W∂T∂U  for W=eUT

Q: List the sides of AFGH in order from least to greates if mZF=(5x+6)°, mZG=(12x-4)°, and m…

A: Consider the following △FGH: m∠F=5x+6°m∠G=12x-4°m∠H=4x+31° Sum of all angles of triangle is 180°.…

Q: (i) Let RW, = {(so.S1.. sn) : So = 0, Isi+1 – Si| = 1,i = 0, 1,...,n– 1} be the set of all possible…

A: We are given the collection of all possible random paths of order n as RWn And the a subset Dn…

Q: Express the following as linear combinations of u = (2, 1, 4), v = (1, – 1, 3), and w= (3, 2, 5). 8.…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.