Express the vector - 4i - 8j + k as a product of its length and direction. - 4i - 8j + k=[Di+ ()j+ (D k )k]

Q: The vector z = (2 + 2i) ( -V3 + i) lies in * the

A: The vector equation is z=2+2i-13+i.

Q: Find a unit vector in the same direction as 8i-j+ 4K

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Q: Find the length of the vector I -6 -5 ||

A: x→=x1x2x3length of vector x→ is (x1)2+(x2)2+(x3)2

Q: Find the vector in AB R2 given in the figure. 6 AB = help 4 (vectors) 1 2 3 -1 -6 -5 -4 -3 -2 -1 6.…

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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: Find the vector equation of the line that passes through (1,0,-3) and it's parallel to v=2i - 4j +…

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

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 6v.

A: Given vector is v = -3i +7j.

Q: what will be the direction of -k x -i ?

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

Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: Which of the following vectors is the scalar multiple of z-(4, 3, -2) ? Ou- (-28, -21, -14) Ou-(-24,…

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Q: 4. Find a unit vector in the same direction as the vector 8i- j+ 4k.

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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: solve for th e vector x in terms of the vectors a and b. x - a= 2(x - 2a)

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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: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: Express the vector as a product of its length and direction. 6j - 8k 100- 10(j - k) 3 10 j O 10(6j -…

A: We have to find out the vector

Q: 2 nogonal to the vector

A: The coordinates of point M is 1,1,0 . The orthogonal vector to M is 200. The equation of the plane…

Q: Find the vector in the same direction as <1, 1, 0> whose component in the direction of <2,…

A: Let  us suppose that

Q: Show that the vectors are orthogonal.

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Q: a = 3i - 2j + 5k and b = -2i-j+k, find 2a-3b and also its unit vector.

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Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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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: 2. Sketch the vector v = 4i – 6j. 1아 6 4 2- 10 -8 -6 -4-2 2. 4. 6 8 10 -2 -4 -8 C0 10

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Q: 2) Subtract the (2) vectors; (4, 6) & (-8, -10)

A: The given vectors are 4, 6 and -8, -10 We need to subtract the given vectors.

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: 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: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find specified vector or scalar||-2u||.

A: given that u=2i-5j v-3i+7j w=-i-6j

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: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 3u + 4v.

A: Given: u=2i-5j,v=-3i+7j and w=-i-6j. To find: 3u+4v Solution:…

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: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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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: 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: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 5v.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: The vector or scalar 5v. Solution: When we…

Q: 1. a. If 37-2ỷ = ở and 5x - 33 = b, express the vectors and y in terms of a and b. %3D %3D

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Q: Determine the vector component of the vector 3i-4k on the vector 4j+3k.

A: Given two vectors are: a→=3i-4k                                    &    b→=4j+3k

Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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

A: Use the decomposing concept of a vector.

Q: Express the resultant vector as a linear combination. f=-3i - 10j %3D g = 11i + 5j Find:-6f +2g

A: To find -6f+2g.

Q: For the vector r (3, - 1), what is -4r? The vector - 4r = ( ).

A: Given :   Vector r =  ⟨3, -1⟩  To find : -4r ?

Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 4u - (2v - w)or scalar.

A: To Determine: find 4u-2v-w Given: we have u=-2i+3j  ,v=6i-j  ,w=-3i Explanation: we have…

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: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.

Q: 3- Rewrite the vector v in the form a + ib, where vectors a and b have only real components.

A: