For this problem, consider the points P = (-2,8,9) and Q = (0, 4, 5). (a) Express the vector PQ as the difference between two vectors, and then compute its coordinates. (b) Compute a unit vector u in the same direction as PQ. (c) Compute a vector v of length 10 in the same direction as PQ.

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vectorA 2i-j+ 3k…

A: I am attaching image so that you understand each and every step.

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

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Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

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A: Solution:Given   i+2j+kTo express in terms of its length and direction.u=vvand v=vu

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A: When you divide a vector by its magnitude you get an unit vector along its direction.

Q: Determine the two unit vectors that are orthogonal to v = (1,2). Which two unit vectors are parallel…

A: Let the required unit vector orthogonal to v be <x,y>

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A: To find: the vector v of length 2 making an angle of 30◦ with the x-axis

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Q: Find a non-zero vector perpendicular to the vectors and ú =

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Q: Find the vector equation of the line that passes through (1,0,-3) and it's parallel to v=2i - 4j +…

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

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Q: Find two vectors v1 and v2 whose sum is (2, –5), where vj is parallel to (5, 2) while v2 is…

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Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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Q: Find a unit vector in the direction of vector (v= ai + bj ) and orthogonal to the vector ( u= 3i -…

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: is The unit vector in the direction of v=(4,0,–3)

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Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Which two vectors are perpendicular to both a and b?

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

A: Question is solved.

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A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

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Q: Find two linearly independent vectors perpendicular to the vector 4 v =

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Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 4 1 - x + 2y + z = 5 3 Find the normal…

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Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: how can i learnd about vector in r2 and r3?

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Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

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: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: Find two independent vectors both of which are perpendicular to i = 3

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

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Q: The vector from the origin to point A is given as 6ax – 2a, – 4az, and the unit vector directed from…

A: Given vector is A→=6,−2,−4 and B→=B23,−23,13 And B−A=10 We have to find the coordinates of the point…

Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

Q: Which two vectors are perpendicular to both å and b?

A: result of vector cross product of two vector is perpendicular to both the vectors.

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Q: For the vector r (3, - 1), what is -4r? The vector - 4r = ( ).

A: Given :   Vector r =  ⟨3, -1⟩  To find : -4r ?

Q: Find the given vector. Vector v of length 4 in the direction of = (-4, -4)

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Q: Find two linearly independent vectors perpendicular to the vector i = |3

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