Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z. Clearly show why your answer is acceptable.

Q: The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is

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Q: Find the vector with length 3 making an angle of 7π/4 with the positive x-axis.

A: Given that the vector with length of 3 makes an angle of 7π/4 with the positive x-axis.

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: For the three vectors a, band, it is found that ax statement below is true?

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Q: Find the vector of length 2 making an angle of 60° with the x-axis.

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Q: Find two vectors v1 and v2 whose sum is (2, –5), where vj is parallel to (5, 2) while v2 is…

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Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: Find two vectorsī and 02 whose sum is (2, –4), where v, is parallel to (2, -4) while vz is…

A: We have to find vector v1 →and v2→   the sum of vector v1 →and v2→ is 2, -4   vector v1 →is parallel…

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: 10

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Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: Find the vector with length V17 and same direction as = (7,0, -6).

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Q: How do you find the cross product a x b of two vectors if you know their lengths and the angle…

A: If you know the length of the two vectors a and b then, you essentially know |a| and |b| And then…

Q: Find a vector of length 5 in the direction opposite that of (3, –2, V3).

A: Let the given vector be              a=3i-2j+3k The vector in the direction opposite to a  is  -a.…

Q: The vector (3, -1, 2) is parallel to the plane 6x – 2y + 4z = 1. - %3D

A: Use formula to calculate equation of plane

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

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Q: For the vectors u = (- 1,3) and v= (- 4,2), calculate proj,u and scal,,u. proj,u = ( -2,1) scalyu

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Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Find the angle between the vectors (4, 2) and (7, -2). Carry your intermediate computations to at…

A: solve the following

Q: The vector with terminal point at P(-5,0,3) and initial point at Q(6, 2, –8) is equal to the…

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Q: If I was given two-equation of two planes. To find a vector parallel to the plane, do I take the…

A: Suppose the equation of two planes are given. Find out the corresponding normal vectors to the given…

Q: Find the angle between the vectors (2, 1) and (3, -2) to the neareast second.

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: Find the vector that has the same direction as (2, 6, -9) but has length 4.

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Find two vectors and 02 whose sum is (2, –4), where is parallel to (2, -4) while vz is perpendicular…

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Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

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Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Find the vector of length 2 making an angle of 45° with the x-axis.

A: Find the vector from the given data

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: Find the area of the parallelogram defined by the vectors ä= (2, -2,0) and 6= (0,1,2)

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Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

Q: Find a unit vector perpendicular to both (3,-2,4) and (-1,2,-3).

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Q: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: Find two vectors vj and 2 whose sum is (-2, -5), where is parallel to (-3, 4) while vz is…

A: Solution: The objective is to find the vectors

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

A: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…