6 2 Show that it is vectors are lineas dependent line or independent.

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

A:

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Determine which sets of vectors are orthogonal.

A: Consider the given vector as -312, 241 and 1-12

Q: Suppose that u and v are vectors in R' both of length 2/2 and that the length of u – v is also2 /2.…

A: The solution is give as

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

A:

Q: 2) L is the line passing through points (0, 0, 0) and (1, 1,1). M is the line passing through (2, 3,…

A: Direction vector of the first line is = (1,1,1)-(0,0,0)= (1,1,1) So the equation of the first line…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

A:

Q: 2. 1 show thet vectors cre linecrly dependent or lineerly in dependont

A:

Q: 3. Find a unit vector with the same direction as (3, 4).

A: If we devide each component of vector v by |v| we will get the unit vector Uv.

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: Find the vector v = PQ. Р3 (1,6, 5) Q = (5, 7, 1)

A: To find vector v=PQ→.

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

A:

Q: If P = 1 - 3, 12 and Q = 1x, 42, find all numbers x suchthat the vector represented by PQ >has…

A: Given :               P = (-3,1)   and Q = (x,4)                  PQ→ = Q - P      = x+3,3PQ→= x+32…

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: find the diJ tance betueen the vectors

A:

Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

A:

Q: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

A:

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

A:

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: Find the length of the vector.v = (5, −3, −4)

A:

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

A:

Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

A:

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

A: Given statement is, “A set of three vectors in R4 spans R4.”

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

A:

Q: Show that ū = aitbj is perpendicular to the line ax+by=C by establishing that the slope of the…

A:

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,…

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

A:

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,…

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

A:

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

A:

Q: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: 11) in triple cross of vectors (A x C) x B = C x (B x A).

A:

Q: a) tor which values on a are the vectors 87 2 -- a linearln independent?

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.