If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero , then the value of a is

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Find the cosine of the angle between the vectors P1(x) = 1+ 2x -x² and p2 (x) = -2-x+ 3x2 with…

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

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Describe all unit vectors orthogonal to both of the given vectors. −4i + 6j − 2k,   5i + 4j + 9k

A: Concept: The cross product a x b is orthogonal to both the vectors a and ba = −4i + 6j − 2kb = 5i +…

Q: The cross product of two vectors in R yields a scalar. True False

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Q: 4

A: We are given the following vectors.

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

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Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Find the equation of the plane sanned by the above two vectors

A: Given: Two vectors u=223 and v=-20-3. To find: Equation of plane spanned by given vectors.

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

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Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: the component of vector a are ax=2.0 units and ay=3.0units while that of another vector b are Bx=…

A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

Q: Two vectors ñ and m are said to be orthogonal if ñxm3D0

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

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Q: The ________ ________ of two vectors yields a scalar, rather than a vector.

A: Given as  The ________ ________ of two vectors yields a scalar, rather than a vector.

Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Given: u=23, v=k+1k-1 Concept Used: If two vectors are orthogonal then their dot product is zero.

Q: If the vectors a and b are such that a = kb where k is a positive scalar, then the vectors a and b…

A: Given statement: If the vectors a and b are such that a=kb where k is apositive scalar, then the…

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: Can you find two vectors in R whose dot product is equal to their cross product? No, because the…

A: (iii) can you find two vectors in ℝ3whose dot product is equal to its cross product as we know , dot…

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Two vectors u and v are said to be orthogonal if u·v=0. Given that, u=1-12 and v=k2k-3 We have to…

Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: 3. Find two unit vectors that are orthogonal to both j +2k and į -2j + 3k.

A: Solution is here

Q: Express the vectors in terms of their lengths anddirections. 2i - 3j + 6k

A: The given vector is a=2i-3j+6k. Compute the length of the vector as follows. a=22+-32+62=4+9+36=49=7…

Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: What is the value of each of the constants that are part of the linear combination between the…

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: In Cartesian coordinates, a rank-2 tensor is given by Į = Tr£xx + Tvz£xz+ Tyy£yy and a Cartesian…

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Q: The scalar projection of the vector 7 = (-2, 3, 1) on 7= (2m, -1, 3) is -1. Determine the value of…

A: Follow next step

Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

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