Use vectors to determine whether the points are collinear (3, 4, −1), (−1, 6, 9), (5, 3, −6)

Q: Use vectors to find the point that lies two-thirds of the way from P to Q.

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Q: Use vectors to decide whether the triangle with vertices P(3, -1, -4), Q(4, 2, -6), and R(8, 0, -7)…

A: NOTE: Refresh your page if you can't see any equations. . given vertices are

Q: Find the angle 0 between the vectors. u = (1, 1, 1), v = (7, -6, 5), (u, v) = u1Vı + 2u2v2 + U3v3…

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Q: Express the vector P, P2 in the form v = v, i+ v2j + v3k if P, is the point (- 7, - 3,1) and P2 is…

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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: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

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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 determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find the angle 0 between the vectors. u- (3, 2, 0), v = (-2, 3, 4) radians

A: u=3, 2, 0  &  v=-2, 3, 4 Now, u·v=3-2+23+04=0 Now the magnitudes is,…

Q: Use paper and pencil to identify the redundant vectors. 4 3. 0. 0.

A: Definition : Redundant vector in a set is a vector which can be written as linear combination of…

Q: check whether the set of vectors v1=(-9,-7,-15) ,v2=(1,-1,3), v3=(3,2,5) and v4=(2,1,4) are linearly…

A: The vectors are linearly independent if for the  scalars a , b , c and d,  the linear combination…

Q: Use vectors to determine whether the points are collinear (0, -2, -5), (12, 7, 1), (8, 4, –1) The…

A: Given: (0,-2,-5) , (12,7,1) & (8,4,-1) are three points.   To Check : The given points are…

Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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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: Use vector method to find the area of the triangle with vertices A, B, C that shown in the figure…

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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: Use vectors to determine whether the points are collinear. (4, −2, 7), (−2, 0, 3), (7, −3, 9)

A: Formula: the vectors a, b and c are collinear if detabc=0.

Q: Find the angle θ between the two vectors.u = (3, 3), v = (−2, 2)

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Q: Use vectors to determine whether the points are collinear. (0, −2, −5), (3, 4, 4), (2, 2, 1)

A: A(0, −2, −5), B(3, 4, 4) & C(2, 2, 1) be the given points. Now vector joining the points A and B…

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: Find the angle between the pair of vectors below. u = (2,3) and v = (-2,5)

A: Given query is to find the angle bothe vectors.

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

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Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: ind the cross products u×v and v×u for the vectors u=2,4,0 and v=0,3,−

A: To find the cross products u×v and v×u for the vectors u= (2,4,0) and v=(0,3,−6).

Q: Use vectors to determine whether the points are collinear. (0, –2, –5), (15, 8, 0), (6, 2, –3) The…

A: The given points are 0,-2,-5, 15, 8, 0, 6, 2,-3

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: Use vectors to determine whether the points are collinear. (0, 0, 0), (1, 3, −2), (2, −6, 4)

A: Given:A0,0,0B1,3,-2C2,-6,4

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A: Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)…

Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

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Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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Q: Use vectors to determine whether the points (0, -2, -5), (3, 4, 4), and (2, 2, 1) are collinear (the…

A: Given points are 0,-2,-5 ,3,4,4 and 2,2,1 Let points 0,-2,-5 , 3,4,4 and 2,2,1 be denoted by P,Q and…

Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

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Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

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 angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v . u) –…

A: Given that u=2,2,  v=-5,1  and  w=2,-2.. Compute v·u as follows. v·u=-5,1·2,2=-52+12=-10+2=-8

Q: B: Find area of triangle whose vectors P1(4,2,0), P2(-1,1,1), P3(0,4,3) (

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Q: Find the vector in R' from point A = (-2, –3, 8) to B = (9, –4,–3). AB = help (vectors)

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Q: Determine if the vectors u=, *v= and w= lie in the same plane or not

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Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: find the component form of the vector. The vector from the point A = (2, 3) to the origin.

A: Find the component form of the vector. The vector from the point A = (2, 3) to the origin.

Q: Determine the angle between the vectors a = (4, 5, 2) and b = (-3, 6, 0)

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Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

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Q: Find the angle between the vectors [ -1, 1, 2] and [2,1,-1].

A: Consider the vector: v = −1,1,2w =…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.