Given a vector with initial point at P1 and terminal point at P2 given below, find an equivalent vector with initial point at the origin. Express your solution in terms of the unit vectors i and j.

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: If v = -2i + 5j, find a vector orthogonal to v.

A: Given v=-2i+5j We need to find a vector that is orthogonal to v. Two vectors are said to be…

Q: Find the unit vector in the direction of v and verify that it has length 1.

A: If vector u is given, then the unit vector in direction of vector u is given as,

Q: Express the given vector in terms of the unit vectors i, j, and k. (2, -5, 0)

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Q: Write the following vector as a linear combination of the unit vectors i and j. (-4,Radical 2)

A: We need to the following vector as a linear combination of the unit vectors i and j

Q: Given initial point  P1 = (−2, 1)  and terminal point  P2 = (5, 4),  write the vector v in terms…

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Q: Determine a unit vector perpendicular to the both vectors A : 2i + 5j – 4k and B - 3i + 6k. |0| = (…

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Q: For what value of t, if any, is the vector (8t, 2) parallel to the vector (4, -1) ?

A: Given vectors:A= <8t, 2> and  B= <4, -1>

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Express the vector in terms of the unit vectors i and j. 4) (4,

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Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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Q: find the given vector  Vector of length 2 in the direction opposite to v = i − j

A: A vector oppositely directed to v=i-j is is u=-v=-i-j=-i+j                   u=-i+j A unit vector eu…

Q: Find the component form of the vector v and (b) sketch the vector with its initial point at the…

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Q: Given the vector v has an initial point at (-8, 5) and a terminal point at (-3, –1), find the exact…

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Q: O Find a unit vector (a vector with length 1) that has the direction of 3 2

A: Given below the detailed solution

Q: Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of…

A: See below

Q: ) Write down the position vectors of any two points on the line T·(3i – 4j)+ 2 = 0 and hence find…

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Q: find the given vector. Unit vector in the direction opposite to v = (−4, 4, 2)

A: Given, v=-4, 4, 2

Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: Find the Unit Vector for the given vector ,

A: The given vector is -5,12

Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

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Q: For a given 3d vector, solve for 0, if 0x = 60°and 0, = 45 120° 45° None of these 75° 150°

A: Consider the provided question,

Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: 5) Find a unit vector that has opposite direction of the vector i - 2j + 4k.

A: First change direction of vector then find magnitude and write unit vector

Q: Determine a unit vector perpendicular to both A=i+2j-3k and B=-2i-3j+k

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Q: Find a vector that is perpendicular to both and 2. A =-i - 2j +4k B = 4i - j

A: Take cross product and it's magnitude then find unit vector in perpendicular to both vector

Q: Given initial point  P1 = (−7, 4)  and terminal point  P2 = (9, 6),  write the vector v in terms…

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Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: Find a unit vector orthogonal to the vector A= 2i-j+k and parallel to the vectors B= 2i+2j and C=…

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Q: Find the unit vector in the direction of the given vector a, and express it using standard unit…

A: Find the unit vector in the direction of the given vector a . vector a = 20i - 21j  . Here i…

Q: Given initial point  P1 = (2, 5) and terminal point P2 = (−1, 6),write the vector v in terms of i…

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Q: 13. Find the unit vector having the same direction as v. v = 6i-8j

A: We have to find the unit vector.

Q: (b) Find a vector i that is parallel to ↑ and perpendicular to L.

A: As per your demand, we solve part b) only

Q: 27-j+4k sī +2j-2k.

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Q: Find the unit vector that has the same direction as the vector v = 3i - 4j.

A: We have to find unit vector that has the same direction as the vector v=3i-4j. We know that unit…

Q: Find a vector v parallel to u=−7i+j−6k and with magnitude ||v||=12.

A: Given,          A vector v parallel to u=−7i+j−6k and with magnitude v=12.

Q: Construct the vector 0.6 c+1.7 d having initial point P. (Use the tools provided to move and scale…

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Q: Given a vector v with initial point P(5,12) and terminal point Q(−2,−12), write the vector in terms…

A: vector with initial p1,p2 and                 terminal (q1,q2)is given by v=<q1-p1,q2-p2>

Q: Find the coordinates of the terminal point of the vector v = 3i−2j if the initial (tail) starting…

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Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

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

A: Given:  i + 2j - k

Q: Find the horizontal and vertical components of the vector with the given length and direction, and…

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Q: Express the given vector in terms of the unit vectors i, j, and k. (14, 0, 4)

A: Given,  Vector < 14, 0, 4>

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 a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

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Q: 4) Find the magnitude and direction of the vector i that has components vz -1525 and Vy -8402. %D

A: Any vector lying in the xy-plane, can be decomposed into two vectors which lie along the x and…