Consider the following points P and Q. a. Find PQ and state your answer in two forms: (a, b, c) and ai + bj + ck. b. Find the magnitude of PO. c. Find two unit vectors parallel to PQ. P(3, 8, 12), Q(3, 9, 11)

Q: Find the value of aa in the vector →v=⟨a,b⟩v→=⟨a,b⟩ if b=15 and ||→v||=39|| v→ is in Quadrant I a=

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Q: The following diagram shows the parallelogram ABCD. B A D Let AB =p and AC=q. Find each of the…

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Q: Given the two vectors A = -9i- 2j -7k and B = -3i- 4j +8k, Find th (e) Ax B (f) the angle between…

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Q: In the previous question, what is the angle between the two given vectors to the nearest degree? a)…

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Q: .If the position vectors of the points A, B, C, D are a = i+j+k, b 2i + 3j, c= 3i+ 5j - 2k, d k-j.…

A: Given:  a=i+j+k, b=2i+3j, c=3i+5j-2k, d=k-j We know that if A=x1i+x2j+x3k, B=y1i+y2j+y3k then…

Q: Given 2D vectors a and b such that la= 7 and 1b=8 find the angle between the vectors if: a) la +b| =…

A: topic - angle between vectors

Q: In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

A: Consider the figure shown belowAssume , D is the midpoint of side AB of triangle ABC , and E is…

Q: Given the vectors shown, sketch ủ +v, ū-v, and 2u .

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Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

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Q: A If the magnitude of vector A is multiplied by 2, which of the following vectors would be the…

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Q: Write the vector v in the form ai+bj​, given its magnitude v and the angle α it makes with the…

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Q: For what value of m, the vector 4i + 2j – 3k and mi – j+ V3 k have same magnitude? Q.3

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Q: Given the two vectors A = -9j- 2 -7k and B = -31- 4j +8k, Find the (a) A + B (b) A B (c) -4A…

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Q: Consider the following points P and Q. a. Find PQ and state your answer in two forms: (a, b, c) and…

A: (a) The vector joining two points P and Q is defined as, Where, the vectors P and Q are the…

Q: Let a=⟨−3,2⟩ and b=⟨2,−5⟩Find the angle between the vector, in degrees.

A: Let the angle between a and b is theta So,  We find a.b and |a| and |b| first

Q: If la| = v2, la + b| = v6 and la – b| = v2, find the angle between the two vectors å and b.

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Q: if theta is the angle between the two vectors, v, and w, find the measure of angle theta in degrees,…

A: Use given vectors find angle between them

Q: Write the vector v in terms of i and j whose magnitude v and direction angle 0 are given. Iv=18,…

A: we are going to asume v=xi+yj and then by the given data will find the value of the x and hence…

Q: Consider the following points P and Q. a. Find PQ and state your answer in two forms: (a, b, c) and…

A: We have given two points P0,0,2 and Q-2,4,0.

Q: The vector v has a magnitude of 3 and makes an angle of 30° = π6 with the positive x-axis. Write v…

A: Given that the magnitude=3 and angle is 30° with the positive x-axis.  So,  v=3(cos30° i+sin30°…

Q: Let the angle between two nonzero vectors u and V be 45°, the magnitude of the vectors be a and 2…

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Q: 4. Given a = 5 m and b= 7 m, and the angle between the vectors ā and b is 102°, determine a +b,…

A: As we know that the expression for a→+b→ a→+b→=a→2+b→2+2a→b→cosθ Where; θ is the angle between…

Q: What is the angle of vectors A=5m West and B=15m 60° North of West?

A: The vector A can be written as: a=-5i The vector B is 60 degree north of west that means it makes an…

Q: Obthe resulting parallelogram from the following two vectors that form non-parallel sides A = 3 + 2…

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Q: If U and W are unit vectors in R" and |U - 3W = v13, then the angle between U and W is: O a. 30° O…

A: Option C will be the right answer.

Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

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Q: Consider the points P(2,7) and Q(6, 4). Write PQ as a product of its magnitude and a unit vector in…

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

Q: Given the following points, find the magnitude and direction angle for vector AD A= (3,-2), D=…

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Q: Consider the weight suspended by two wires in each diagram. Find the magnitudes and components of…

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Q: If two nonzero vectors v and w are orthogonal, then the angle between them has which of the…

A: Two non-zero vectors v and w are orthogonal if angle between them is π2. The dot products of two…

Q: Find the magnitude and direction angle of the resultant of each pair of vectors. t = (17, 12) u =…

A: We use vector additions.

Q: If (a,ß.r) is a vector of magnitude 24 and having the same direction as the vector (1,-22,-2), then…

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Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: |미350, | w|= 12, 0=35° A) B) W W

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Q: Use the Law of Cosines to find the angle α between the vectors. (Assume 0° ≤ α ≤ 180°.) v = 7i + 7j,…

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Q: Consider vectors A= -51 + 2j and B = 6î – 5j. Now answer the following questions %3D

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Q: In the rectangular prism shown below, OA=a, OC=b and oD =c. Express each of the following vectors in…

A: We have to express sides of rectangular I  prism in terms of vector a, b, and c

Q: In the rectangular prism shown below, OA=a, OC =b and oD =c. Express each of the following vectors…

A: We have to write following side of cube in vector form on the basis of given vector.

Q: Find the angles between these vectors, giving your answer in degrees to one decimal place. ) -3 and…

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Q: Let →a=⟨−2,−1⟩ and b→=⟨0,-5⟩. Find the angle between the vector, in degrees.

A: We can find the angle between the vectors as below.

Q: Given vector u = 5i – 2j, what is its magnitude and direction? (a) v29; –21.8° (b) v29; 158.2° (c)…

A: The solution is :

Q: For the given vectors: a = (2,–3), b = (0,3), c = (1,4), find: (a) 3å – 6+ 2č (b) angle between the…

A: a) this is the case of scalar multiplication and then addition and subtraction. So 3 times of vector…

Q: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: The angle that the x-axis make with the plane containing the following two vectors is A = 4â – 3 B =…

A: To find the angle

Q: Given that the angle between the nonzero vectors đ = (u,,u2,u3), b = (u3.U2, -u,) is find the…

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Q: Given 2D vectors a and b such that |a|= 7 and |b| = 8 find the angle between the vectors if: a) |a…

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Q: Find the angle θ between the given vectors to the nearest tenth of a degree. ​ U = 16i − 8j V =…

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Q: Find the angle ? between the given vectors to the nearest tenth of a degree. U = 13i + 6j, V = −12i…

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Q: Given two vectors P = 9i + 9j + (-9k), Q = (-6j) The angle between the two vectors is

A: We have two vectors P=9i+9j-9k and Q=-6j. Then the angle between the two vectors.