Given v = (8, –3) and w = (12, -4), find vector projection of v onto w.

Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: If å = v2i +j - k, what is the vector whose alignment a is in the opposite direction and its size…

A: Given a→=2i+j−k We have to find the vector whose alignment a→ is in the opposite direction and its…

Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: 4x-y+5z=0

A: If a line and a plane are perpendicular to each other then the direction vector of the line and the…

Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: Given the vectors ū = (-2, 1, 1) and V = (3, –1, 1), calculate the vector projection of ū onto V

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Q: Given vector u= (-3, 3) and v = (6, –2), determine the value of 4u + v in | component form.

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Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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Q: If v . w = 0, then the two vectors v and w are____

A: If v . w = 0, then the two vectors v and w are____

Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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Q: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Given vector u = (6, –1) and v = (2, –2) , determine the value of u – 2v in component form.

A: Given query is to find the indicated vector.

Q: Consider the following graph. (4, 4) 2 (1, 2) 1 3 (a) Find the component form of the vector v. (v,,…

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Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Given the points C(-4, –5) and D(-1, 1), express the vector CD in terms of i and j.

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Q: Given vector u = (-1, –1) and v = (-1,1) , determine the value of 5v – u in component form.

A: A vector is a quantity with magnitude and direction. Given a coordinate system a vector can be…

Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

Q: Consider the graph provided find the length of the vectors u and i

A: Solution and Explanation is given below....

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: Find the vector projection, Proj;A and ProjĄB When A = i+ 2j + k and B = k. 1.6

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Q: Suppose that u, v are vectors in R³, u · v = 1, || = 1, the angle between u and v is T/3, and u is…

A: According to the problem, we have

Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Which vector is the orthogonal projection of v = 0 onto W = span -2 °() V3 V6 3 V6

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Q: Given vector u (1, 1) and v (6, 2) , determine the value of V + 2u in component form.

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Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 =…

A: First obtain a, where a is the distance between R0 and Q.

Q: a) The line y =- 5x + 9, in VECTOR form (R?).

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Q: Given vector u (-1, 5) and v = (5, 3) , determine the value of 2u – 2v in component form.

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Q: A line L has a direction vector v = 2i t 4j+ v5k and passes through the Find the distance between…

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Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: Find the vector z, given that u = (5, -6, 2), v = (0, 2, 1), and w = (-6, W%3D 1. z = -u + 5v + w 2

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Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

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Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

Q: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectilinear Co-ordinate System CCS-Cylindrical Co-ordinate System SCS- Spherical Co-ordinate…

Q: Find the vector z, given that u = (6, -3, 2), v = (0, 2, 1), and w = (-6, -6, 2). %3D Z = -u + 4v +…

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Q: Given vector u (4, –1) and v = (-1, –5) , determine the value of v + 2u in component form.

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

A: Here, in the question three vectors are given:  w1, w2, b  L is the line defined by the vector w1 We…

Q: Given v = 4i - 3j and w = i - 2j, find the vector projection v onto w projwV = 6i - 3j projwv = 2i -…

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Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.