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

Q: Show that each pair of vectors is perpendicular.     -4i -3j and 6 i - 8j

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Q: Use the vectors shown to sketch u - 3v. (Assume that each point lies on the grid lines and that each…

A: Sketch the vector:  First draw the vector 3v: For -3v, the vector will change its direction.

Q: b a

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Q: 2. Add the vectors by rearranging them and then sketching the resultant. u W a. Add the vectors by…

A: To add the vectors  we should sketch the x-y plane .

Q: unit

A: To get the unit vector that is in the same direction as the original vector v, we divide the vector…

Q: Given the vectors, ū = -3i+2j and = 4i – j, find 4ü-27. %3D (-20,10) (20,-10) (-20,-10) (20,10)

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Q: Find the angle between the two vectors and determine if theY are, or thogonai: ü=5i-33+2k ahd V=-i-…

A: We will use the formula: θ=cos-1u→·v→u→v→First we calculate:…

Q: Give two vectors A=4i+3j, B=5i-2j Find its values and the direction of vector C, which is 2A-B

A: Vector addition

Q: Find the vector 5u-2v given the vectors u = 4i+jand v = 5i-2j. Write your answer in the form ai+ bj.

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Q: Find two unit vectors that are perpendicular to both  j + 2k and i - 3j + 2k  (Enter your answers…

A: Cross product of two vectors give always a perpendicular vector to both.

Q: Example: Find the unit vector p for the given vector 12i – 3j – 4k.

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Q: Find the angles between given vectors. (a) ā = 3i + 4j and b= 5i – 4j (b) a = 3i +4j - 5k and 5= 6i…

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Q: Find the component form of the resultant vector. 1) u =(-11, 2) b=(10,-4) Find: -u - b

A: As per guidelines, we'll solve only one question if multiple questions are asked. If you need any…

Q: For the two vectors a = 7i-4j+2k and b = –6i+3j-5k find the scalar component, comp,b

A: a=7i-4j+2k & b=-6i+3j-5k Now, a·b=7-6+-43+2-5=-42-12-10=-64 & a=72+-42+22=49+16+4=69

Q: 16. 7 -7 – 37 – k

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

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Q: Find the components and length of the following vectors:(a) 4i + 3j

A: Given4i+3jTo find component and length

Q: Use scalar product to find the angle between the two vectors A = 2.00i + 3.00j + 1.00k B = - 4.00i +…

A: The given vectors are  A=2i+3j+1kB=-4i+2j-1k

Q: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C = ix - iy + iz Find the following:…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: a)a→=-3 i + 8 jUnit vector as the same direction;u= a→a→ =(-3 i + 8 j)(-3)2+(8)2u=(-3 i + 8…

Q: Find the length of the vectors. (i) 5i - 5j - 3k (ii) 1.4i + 0.6j + 2.8k

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Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

A: Given Vectors are                                                 M=4ax-6ayN=6ax-2ay-5az vector…

Q: 4) -16i + 30j

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Q: Consider the vectors ä = 5i+ 3- k, 6= 5i – 3 + k, 1+53+ 6k d = i+3+6k, j = -1-53+ k. Which pairs (if…

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Q: Find the unit vector and noim of V= 31 +5; -9k .

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Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

A: For a given vector v→, length of the vector is denoted by v→  and direction vector is obtained by…

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k ;

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Q: Given two vectors A = 2i + 3j- 2k B = 3i- 4j- 6k Determine the vector that defines the direction of…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;

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Q: Solve for the vector x in terms of the vectors a and b. x - a = 2(x - 2a)

A: Given: x-a=2x-2a

Q: Given two vectors A = 21 + 3j - 2k B= 31- 4j – 6k Determine the vector that defines the direction of…

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Q: Which of the following vectors represents - 2u + v?

A: Given,

Q: Given the vectors, a = (4,-5) and b = -10i -8j: %3D a. Find a - 2b.

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Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: Find the length of the vectors (a) –2 i + 2j – 4 k: length = (b) 0.47 – 0.4 + 1.6 k: length =

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Q: Find the length of the vectors (a) i +3j+ k: length = (b) i — 2.6 j + 2.6 k. length = -

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Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: 3Q Express each vector as a product of its length and directions i. 2i+j-2k ii. 3/51+4/5k iii.…

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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: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j - 6k du

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Q: Determine the vector 2a – b if a = -4i + 5j and b = 7i + 2j. %3D

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Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. Enter the vector i as i,…

A: here here we have

Q: (B): Find the unit vector perpendicular to the vectors: 4i + 5j - 6k 3i - 4j+5k ;

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Q: Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

A: Topic = Vector

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j - 6k du ;

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Q: Find the unit vector of 4a where a3(4sin 0,-4cos 0,0).

A: It is given that a→=4sin θ ,-4cos θ ,0.

Q: (b) Find the sum of the vectors 3î + 7ĵ – 5k, 2î – 3j – 8k and i- 2j + 12k. Also calculate the unit…

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Q: If a = 3i-j-4k, b - 2i + 4j-3k and c i+2j-k. Find unit vector parallel to 3 a -2 b +4 c. Q.1

A: Comment:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: ä = 27 + 6j – 4K, b = -3ï – 9j + 6K

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.