Let ->u = (2, 1, -1) and ->v = (0, 2, 3). Find the projection of ->u onto ->v and the unit vector along the direction of ->u.

Q: The component of the vector (-5, 0, –3) onto the vector (3, –4, –2).

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Q: Find a unit vector that are orthogonal to the vector (2,−3,1), (5,−2,0), and (3,0,1)

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Q: Let u be the vector with initial point (2, -5) and terminal point (-1, 3).  Find the norm (or…

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Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

A: Initial point is (3,2) and the ending point is (5,6) so the vector is u=(5,6)-(3,2)=(2,4)   Initial…

Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

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Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1) for…

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Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: Find a unit vector u in the direction of v. Verify that ||u|| = 1. v = (-6, 6)

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Q: For the vectors u= (-3,0,4) and v= (1,3, - 3), calculate projyu and scal, u. proj, u = OOD

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Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

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Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

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Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: Find the vector with length V17 and same direction as = (7,0, -6).

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Q: find vector v that is orthogonal to vector (0,1,0,0,0) Select one: a. v=( -1, 0, s, t, w) b. v=( r,…

A: Two vector are orthogonal if their dot product is zero.

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: The vector v and its initial point are given. Find the terminal point. = (4, -9); Initial point: (9,…

A: Given

Q: Find the vector with initial point P and terminal point Q: P= (2,-3) and Q= (0,5)

A: Simply substrate the given two points fro one another.

Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: Let u be the vector with initial point p( 5,1) and terminal point q ( 2,2,) express u in terms of i…

A: NOTE: Refresh your page if you can't see any equations. . the initial point is  and the terminal…

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) with…

A: Given vectors u=(1, -3, 5)  v=(2, 1,-3)  And line passing of point (1, 2,3)

Q: Find a unit vector that is anti-parallel to the vector (1,2,0,3).

A: A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude…

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

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Q: A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1) for…

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Q: Let u be the vector with initial point 〈-2, 6〉and terminal point 〈-8, 3〉. Write u as a combination…

A: Let, x=<-2,6>=-2i+6jy=<-8,3>=-8i+3j

Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

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Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

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Q: If vector u has initial point (3,0) and terminal point (7,-2), find the linear combination of vector…

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Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: a) Find vector equation and paramedrie equahion for the line that passes through the point (5,1,3)…

A: The objective is to find the vector equation and parametric equations for the given problem

Q: A vector orthogonal to the plane through the points (-1,0,0), (0,0, –2), (2,3, 4) is О О O 6,-10, 3>…

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

A: This is a problem related to vector. Based on the general concept and formula we will answer the…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: Find a unit vector orthogonal to both u and v. u = (-4, 5, -2) v = (-1, 1, 0)

A: The vector which is orthogonal to both u and v is defined as u×vu×v. Here, u=-4,5,-2 and v=-1,1,0.…

Q: Let u, = (1,1,1)", u2 = (1,2,2)T and uz = (2,3,4)", find the coordinates of the vectors (2,3,2)" and…

A: Solving by linear combination method

Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).

A: Explanation of the answer is as follows

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: Let x be the unit vector parallel to the vector from the point (2, 3, −2) to the point (-6,2,2).…

A: To obtain the direction vector of the unknown vector obtain the direction vector of the vector…