Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has a positive r-component.

Q: show that the vectors: 2,3), II

A: To prove that the vectors:     v1=(1, 2, 3), v2=(-2, 1, 1), and v3=8, 6, 10 in ℝ3  are linear…

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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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: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Find a unit vector parallel to the line y = 7x – 3. Use the scalar product to find the angle between…

A: The equation of given line is:.Suppose,.So,.So, the parametric equation of the line is:So, the line…

Q: y 3 2 1 O -1 -2 -3

A: Given query is to find the x component of the vector.

Q: Let u= and v=. Give two vectors that are perpendicular to both u and v.

A: Consider the vectors

Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

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Q: Find the B-coordinate vector fe

A: First multiply some constant with given coordinator polynomial and equal the vector p(t) and find…

Q: Find a unit vector with the same direction as the vector u = (7, 4, −3)

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Q: Find the vector equation of the line that contains the points (-17, 10,2). r(t)= ( ) +t ( and

A: Answer :

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 5v

A: Given that u=-3, 4  and  v=2, -5. This implies that, 5v=5·2, -5=5·2, 5·-5=10, -25 Thus, the…

Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

Q: Find the unit vector with the opposite direction of a⃗=(8,−10,3,−1,9,3)

A: We have to find the unit vector with the opposite direction of a→=8,-10,3,-1,9,3.

Q: Find a unit vector u in the direction opposite of (-1,-9, –7). | u =

A: First we find the vector of the same magnitude in the opposite direction of the given vector and…

Q: Find two linearly independent vectors perpendicular to the vector 15 "I G.

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Q: Let ū = -27+ 95 and v = 4i- 7j. Compute each of the following. %3D (a) 2u – 30 (b) ||ū+ T|| Find a…

A: Note: As per company guidelines we are supposed to solve only 1 question. So, kindly repost other…