Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which valuc of x are v =< 1,3, 5 > and w =< 3, x, –1> orthogonal?

Q: Graph and find the area of the parallelogram formed by the vectors u = and v = .

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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: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Find a vector, w, which is perpendicular to the vectors where u = 101-20 +14k and v=-20 +10ĵ-5k W +…

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Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: Let J = 31 +43 - K and ✓ = 2₁ +3₁-2k be of two vectors. Find the component and projection U in the…

A: u→=3i+4j-k,v→=2i+3j-2k

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

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Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

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Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

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Q: Find the angle between vectors a= (-/2, 0, v2) and b = (-1,1,0). %3D

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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: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

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Q: Determine the angles between the following pairs of vectors. (a) (−1, 1), (0, 1)     (b) (2, 0), (1,…

A: To determine the angles between the following pairs of vectors.

Q: Find the angle between the vectors a = 77 +37 +27 and 7 = 27-7+ k.

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Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors &lt;1,1,0&gt; and &lt;0,1,1&gt; to get a cross product for a…

Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: Find the angle between vector [2, −5,7] and the x-axi

A: topic- angle between vector and x axis

Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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