A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector (9,12,0) parallel to P1P2 or not?

Q: Suppose A and B are non-zero vectors in R. If A•B = 0, then A and B are parallel. True False

A: Follow next step

Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: Two vectors in R- are linearly dependent if and only if they lie on a line through (0,0). Select…

A: It is false.

Q: Find a vector v satisfying 3v + (5, 20) = (11, 17).

A: To find a vector v satisfying 3v+(5,20)=(11,17).

Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: If k is a real number, then the vectors (1, k), (k, 5k + 14) are linearly independent precisely when…

A:

Q: Suppose u = (-6,4, –5). Mark each vector below with a "T" if it is perpendicular to u, and an "F" if…

A: The given vectors u=-6, 4,-51. 2, 3, 02. 5,-2, 23. 9,-24,-304. -5,-4,-1

Q: Which of the following vectors is not parallel to v = (4, -2, 1). Choose all that apply. %3D O (8,…

A: We know that a vector a is parallel to vector b if a can be expressed as scalar multiple of b. Given…

Q: To express the vector =(1.2 -6) as a linear combination of three vectors ,- (0.1. 2), v= (1,0.2) and…

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Q: a) If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4), v…

A:

Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). OF (t) =…

A: Note that the vector equation of the line passing through two points a→ and b→is given by:…

Q: The norm of the vector v = (-4, 4, -5, -3) is O y66 O 30 O y6I 66 O 61 O y30 O7 O None of the other…

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Q: 1. Show that the set as; S = {(1,1,1), (2,3,3), (0,1, 2)} spans R3, write the vector (4, 6, 7) as a…

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

A: To find vector v=PQ→.

Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: find the components of the vector −→P Q. P = (1, 0, 1), Q = (2, 1, 0)

A: Given  P=<1,0,1>Q=<2,1,0> The component form of a vector is the ordered pair that…

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Express the vector v = (3,2,7) as a sum…

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Q: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

Q: Show that the set as; S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a…

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Q: Find a vector perpendicular to d = [5,–4,6] and h = [-1,3,9].

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Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

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Q: Suppose that ā and b are nonzero vectors. Under what circumstances is comp;b = comp;a? Under what…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: Let v1, v2, vz be the vectors in R defined by 30 -17 7 -3 v2 15 V3 = -14 -12 -14 18

A: Solution is given below:

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

A:

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

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Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: Find the length of the vector.v = (2, 0, −5, 5)

A:

Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

Q: a- Show that if v is any nonzero vector then is a unite vector . |||| b- If u = (3,4) , v= (3 ,-1)…

A: First assuming v in vector notation.

Q: Let P and Q be the points P (2, – 6) and Q (9, – 6). Find the vector PQ in componert- form:

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Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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Q: b) Express the vector (–1,5, –6) in R³as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A:

Q: Find the vector z, given that u = (5, -6, 2), v = (0, 2, 1), and w = (-6, W%3D 1. z = -u + 5v + w 2

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Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

A:

Q: - Find the length of the vector -3v if v = (2, 3, -2, 1).

A: Givenv=(2,3,-2,1)-3v=(-6,-9,6,-3)

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

A:

Q: Find the length of the vector v = (1, 1, 7).

A: Given : v = 1, 1, 7

Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: Find the vector z, given that u = (7, 6, 7), v = (2, 2, –1), and w = (4, 0, –4). z -u -v + 2w

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.