IdConsider æ, y, and z real numbers. Identify correctly the following. f:R^3 f(t)=(g(t),h(t),j(t)) it is a vector in 3 dimensions f:R^3 R^2 f(x,y,z) is a real number f:R R^3 f(x,y,z)=(g(x,y,z),h(x,y,z)), each g(x,y,z) and h(x,y,z) are real numbers. f:R -R f(x) is a real number

Q: (b) ||ū× w|| (u • w) (c) (d) (r+s) ux v + w s(v+w• w) × (rv)

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Introduction: The coordinate of a point x,y,z is actually the components of the position vector…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Solution:-

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: (d) (0, b) (e) (c -d) (f) (-, g)

A: Let T:R2→R2 be a reflection in the line y=x.

Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: 7. The vector equations of two lines Li and L2 are given by L4: r =i-j+3k+ A(i – j + k) L2: r = 21 +…

A: We will be using fundamental concepts of 3D geometry.

Q: Find the vectors direction of F= -2yi-xJ of the points below :- (-12-1), (-21-1),(3,0). (-1₁-2),…

A: Vector, F→=-2y i^-x j^Points: -1, -1, -2, -1, 3, 0, -1, -2, -3, -2, -1, 0

Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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Q: The vector describing a particular particle is given by F (t) = Rcos (wt) î + R sin (wt) ĵ, where R…

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Q: (d) s(v+ww) × (rv)

A: Given that u→,v→,w→∈ℝ3 and r ,s ∈ℝ.

Q: Do question one only

A: (a)…

Q: Consider vectors u and v. Find the following. (a) u v (b) u.u u = (-3, 0, 3), v = (-1, 6, 1) (c)…

A: The given vectors are

Q: Current Attempt in Progress Find the scalar triple product u · (v x w). u-(-8,4,4), v- (5,1, - 4), w…

A: Given: u=-8,4,4, v=5,1,-4, w=-7,4,3 To find: u·(v×w)

Q: -2st] Let W be the set of all vectors of the form 3s + 5t t - 2s H v = Find vectors ū and 7 in R³…

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Q: Zero component of the curl For what vectors n is(curl F) ⋅ n = 0 when F = ⟨y, -2z, -x⟩?

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Q: Let u= (2,-3, 2, 5) and v a- i b- = (1, 2, 0, -4). Find scalars a and b so that au + bv = (0, -7,2,…

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Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: i. BC if x = 2 and y =2

A: In right angle triangle BOC.

Q: Question Two (a) Prove that the vector field F(x, y, z) = (x² + y²)i – 2y(z+=)j + (zy +2²)k is…

A: The given vector function is, F=x2+yzi-2y(x+z)j+(xy+z2)k. To Prove: this vector field is…

Q: 9. Find the vector triple product of vectors u, v and w. =(2,-1,3), v=(0,1,7), w=(1,4,5) (a) ux(vxw)…

A: The solution of the problem is given in the next steps.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: a State the condition(s) that a, b, c, and d must satisfy for the vector b to be 1 1 -1 and spanned…

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Q: - Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in…

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Q: Consider the vectors v₁ ví = (1,2,3,0), v = (0,1,2,3) and vg = (2,3, 4, -3) Let (1, 1, 1, 1) w (a)…

A: