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

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Find a unit vector that are orthogonal to the vector (2,−3,1), (5,−2,0), and (3,0,1)

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Q: Find the dot product of the pair of vectors (-2, 5) and (4, 1).

A: Given : < -2 , 5 > and < 4 , 1 >

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: 2. Find the volume of the parallelepiped formed by vectors d (-1, 2, 1), 6 = (3, –2, – 1) and T =…

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Q: Find the volume of the parallelepiped spanned by the vectors a =(-2,3, 1), b = (0, 4, 0), and c =…

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Q: Find the unit vector that has the same direction as vector v that begins at (1, 4, 10) and ends at…

A: We will find the unit vector that has the same direction with the given vector v in the following…

Q: Find two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Find the volume of the parallelepiped determined by the vectors å = (3, 4, – 1), 6 = (0, 2, 1), c =…

A: The volume of the parallelepiped  determined by the vectors a, b and c is given by a·b×c or…

Q: Find the volume of the parallelepiped determined by the vectors = (1, 2, 3), b = (3, 0, 6) and c =…

A: This question is related to vectors, we will solve it by using the formula of volume of…

Q: Find two unit vectors parallel to (2, 3).

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Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ 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 the volume of the parallelepiped determined by the vectors a c = (2, 3, 1). Volume =…

A: The volume is given by scalar triple product of vectors. a→=4,2,-1, b→=0,3,2,c→=2,3,1

Q: Find the volume of the parallelepiped determined by the vectors a č = (2, 4, 1). (3, 5, – 1), 6 =…

A: The volume, V , of a parallelepiped is calculated using the scalar triple product, V=c·(a×b) . Use…

Q: Find the area of the parallelogram that has the vectors as adjacent sides. u- (3, -5, 3) v = (2, 0,…

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Q: Find the area of the parallelogram whose diagonals are represented by the vectors a =(3,-3,1) and b…

A: See this solution in below

Q: Find the volume of the parallelepiped determined by the vectors a = (2, 3, – 1), 6 = (0, 2, 1), c=…

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Q: Compute the distance between the vectors u = and v = 315

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Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

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Q: Find the area of the triangle with vertices (3, 7, 1), (4, 2, 1), and (3, 1, –6). Then find both…

A: Vertices of a triangle A(3, 7, 1), B(4, 2, 1), C(3, 1, -6) AB→=(4, 2, 1)-(3, 7, 1)      =1, -5, 0…

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

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Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

Q: Find the smallest positive angle between the given pair of vectors. (3,1) , (4,6)

A: The given pair of vectors are,

Q: Apply Gram- Sch maidt process to the vectors [ (7,

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Q: Find the area of triangle with the vectors p(0,1,4),0(-5,9,2) and R(7,2,8)

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Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ‹6, 2, -1›,     b…

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Q: Find the measure of the angle between the two vectors. (-4, 5) (-6,3) ►

A: Consider the graph

Q: Determine the volume of the parallelepiped formed by the vectors P = (2,4,3), Q = (1,3,2) and R=…

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Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

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Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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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: Find the volume of the parallelepiped defined by the vectors: a= (3, -1, 1), b= (4,0,2) and c=…

A: Given are the vectors  a= (3, -1, 1), b= (4,0,2) and c= (-1,-2,-3) The objective is to find the…

Q: Find the volume of the parallelepiped determined by the vectors (0, 4, 5), (2, 0, 5), and (-1, 3,…

A: Volume of parallepiped is (a X b).c

Q: Find the volume of the parallelepiped defined by the vectors 2 4 -4 -2 4 3.

A: We have to find volume

Q: Find the volume of the parallelepiped determined by the vectors a= (3, 2, - 1), b = (0, 4, 3), č =…

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Find the area of the parallelogram whose diagonals are represented by the vectors a = (3,-3,1) and b…

A: As we know that; The expression for the area of the parallelogram with the diagonals a→ and b→.…

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

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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 two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors <3,1,4>, <2,0,2> and…

Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

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: 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: The dot product of two vectors is a ________ quantity. For this reason, it is some-times called the…

A: Let A and B be two vectors, the dot product is defined asA.B=ABcosθ, where θ is the angle between…