For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax (B x C) = B (A · C) – C (A · B) b) Find unit vector in the direction of A vector

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: Determine and construct the vector c= a x b, where (1) a = 3 i and b = 2 k. (2) a = i +j and b = i…

A: To determine c=a×b 1 a=3i^, b=2k^2 a=i^+j^,  b=i^-j^3 a=2i^+3j^,  b=3j^+2k^

Q: Let ā= −i − 2j + 3k, b = i - 2j + 3k, c = −i +2j - 3k.

A: The given vectors .The objective is to find the vector that is perpendicular to both  and .

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

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

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Q: Q11: Let vector v = (-7, 5) and vector w=(2, 2). Write vector v as the sum of two orthogonal…

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Q: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

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Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

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Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

Q: Find a unit vector with positive first coordinate that is orthogonal to the plane through the points…

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Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

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: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: All v's, w's, i's, and j's are vectors) Let v =⟨2,4⟩ and w =⟨3,−5⟩ (a) Find a vector of unit length…

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