13. (а) What is a unit vector? (b) and 6 = (2, –2,3). Determine the components of a unit vector that is perpendicular to both đ = (1, –1, 1)

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: What are the components of vector p which has three times the magnitude of the normal vector of the…

A: Given plane: Let the normal vector be n. So,

Q: ind a unit vector orthogonal to bothu and v. u = (-8, 7, -2) v = (-1, 1, 0)

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Q: Find a vector ū that is parallel to the yz-plane and perpendicular to the vector i = (0, 2, 2).

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Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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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: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

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Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: What is the i-component of unit vector of the vector u ? Give your answer correct to two decimal…

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: A vector is in standard position if the _____ of the vector is placed at the ______ ofa rectangular…

A: To fill up the blanks,  A vector is in standard position if the _____ of the vector is placed at the…

Q: Find the vector equation of the line that passes through point M(1, 1, 2), intersects the following…

A: Question is solved.

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: Find a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection,…

A: We have to determine the vector that specifies the velocity at which the pathogen is evolving…

Q: 19. Find two unit vectors perpendicular to vector u= (7, 0, -1) and vector v = (1, -1, 1).

A: We have to find the unit vector

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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Q: What is the magnitude of the vector v with initial point P = (-4, 3) and terminat piont Q = (2, -5)…

A: A detailed solution is given below

Q: 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

A: Given a=i+2j-3k b=2i-j+4k Aim : to find unit vector perpendicular to a and b

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: d a vector orthogonal to both u and v.

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Q: 1 If vector is a unit vector, what is the x?

A: We will find the value of x as following.

Q: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

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Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

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

Q: When is a vector incomprehensible and when is a vector irrational?

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Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

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Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

A: