If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the vector and a given scalar k.

Q: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

A: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

Q: How are a vector and a scalar different?

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Q: express each vector as a product of its length anddirection. 2i + j - 2k

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Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: Let a = (10,-1,1) and b = (5,-3,-9) be vectors. How do I find what the image is asking for?

A: (A) ⇒Projb→a→=a→·b→a→⇒Projb→a→=(10, -1, 1)·(5, -3,…

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

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Q: Find two vectors that are not multiples of each other and are both orthogonal to〈2, 0, −3〉

A: Consider the first vector, and the second vector, x1,y1,z1 and x2,y2,z2, respectively. Since both…

Q: Find the magnitude of the vector. (-3, – 7)

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Q: Express the given vector in terms of the unit (о, -5, 7)

A: Given query is to express the vector inthe form of unit vector.

Q: 1. Determine the dot product of the two vectors in the diagram.

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Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: We say that two vectors are equivalent .if they have the same components

A: Ginen statement, Two vectors are equivalent if  they have same component.

Q: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

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: Let a, b, and c be three-dimensional vectors. Identify whether the expression a- (b- c) will result…

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Q: Find the magnitude of the given vector. (-3, 6, 2)

A: Given,            The vector is <-3,6,2>.To find : The magnitude of the given vector.We know…

Q: Find the vector pointing in the direction opposite that of (6, –8) with length 20.

A: The given vector  6,-8 For a given vector v, to find a unit vector u in opposite direction of v…

Q: Write down the 2 by 2 matrix that a) project every vector onto x¡ axis. b) rotate a vector clockwise…

A: We have to solve given problem:

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: Find the vector that has the same direction as (6, 2, -3) but has length 2.

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Q: Find the vector that has the same direction as (3, 2, -6) but has length 5.

A: Just follow the flow and you are done.

Q: Find a vector in the same direction as (-5, 2, –3) with magnitude 6.

A: In this question , firstly we can find the unit vector of the given vector and after that we can…

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: 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: ) Find a unit vector with the same direction as (1,0, 7).

A: We can find the unit vector as below.

Q: Are the vectors -5 -3 and 4 linearly independent? Choose If they are linearly dependent, find…

A: Here we have to check the given vectors are linearly independent or not.

Q: he vector as a

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Q: Find the length of the vector. v - (9, 12)

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: True/False: Vectors are completely determined by their magnitude. In contrast, scalars are…

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Q: Find the unit vector with the opposite direction of a⃗=(8,−10,3,−1,9,3)

A: We have to find the unit vector with the opposite direction of a→=8,-10,3,-1,9,3.

Q: Express the vectors in terms of their lengths anddirections. √2i + √2j

A: If a vector is defined as: v→=ai+bj Then, the length or magnitude of the vector is: |v→|=a2+b2 The…

Q: Express the vector -8i-4j-8k as a product of its length and direction.

A: Given vector v→=-8i-4j-8k

Q: Given the vector A 2i +3 j, what is 3 A? Expand vector and collect like terms (simplify).

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Q: Let a, b, and c be three-dimensional vector5. Identify whether the expression ax (b x c) will result…

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Q: The vectors 2 and are given by 1= 21+4j-k m and --3i+5k m. Detemine the scalar and vector product à…

A: on solving this we get

Q: Illustrate and explain how to compute the vector product of two vectors.

A: Given query is to find explain vector product.

Q: when we decompose the vector , what would the vertical component be?

A: Use the decomposing concept of a vector.

Q: Find a unit vector that is orthogonal to both >= 2i - 10j + 8k & v> = 4i + 6j – 8k Upload Choose a…

A: Explanation of the solution is given below...

Q: The number of elements in a vector generated by [4:0.1:13] is

A: We have to find the number of elements in a vector generated by  [4 : 0.1 : 13].

Q: .3

A: Given: v={ √2,3√2}

Q: Find the scalar component of 6 a, +2 a,-3 a, along 3 a,- 4 a,

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Q: If a vector V is in standard position and the tip of the vector corresponds to the point(a, b), then…

A: Given, If a vector V is in standard position and the tip of the vector corresponds to the point(a,…

Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1