Consider a slanted plane that intersects the entire x-axis and also contains the point P ( 1 , 2 , 4 ). a. Draw this plane, then find and label the coordinates of two other points in the plane. b. Draw two non-parallel vectors that lie in this plane, and find their components. c. Find a vector that is orthogonal to your two vectors. This is called a normal vector for the plane because it is orthogonal to every vector in the plane.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: point = (3,5,-7)n=0 i +1 j + 0 kCartesian equation of plane is Ax+By+Cz+D=0(A,B,C)=( 0,1,0)(x,y,z) =…

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Q: The lines L₁ and L2 meet at the point P. The line L3 is coplanar with L₁ and L2 and is perpendicular…

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Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

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A: Given that, a⇀=i^+j^+k^ b⇀=mi^-k^ Then we get, a⇀·b⇀=i^+j^+k^·mi^-k^a⇀·b⇀=m+0-1=m-1 Moreover we get,…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Given the points P (1, 2, 2), Q (2, -1, 4), R (3, 5, -2) and S(0,-1,3). (a) Use vectors to calculate…

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

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A: Given points are P(2, 7) and Q(6, 4).

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Q: Find a vector V of a magnitude equals 14 and perpendicular To the plane in space which includes the…

A: Explanation of the answer is as follows

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A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 %3! +3y +z 8 Find the normal vector, n,,…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 6t, y = 8 –…

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A: we have to solve given problem:

Q: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v+ w.

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: Linear algebra

A: From the given information:Let,

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Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

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Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

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