4. Point A(-4,2,5) and the two vectors, Ram = 20a, + 18ay – 10a, and RAn = -10a, + 8ay + 15az, define a triangle. A. Find a unit vector perpendicular to the triangle. B. Find a unit vector in the plane of the triangle and perpendicular to Ran- C. Find a unit vector in the plane of the triangle that bisects the interior angle at A.

Q: The dot product of vectors p = (3, -5) and q = (15,9) is A/

A:

Q: Find the area of the parallelogram that has the vectors as adjacent sides. AB= 6i + 6j - 6k, AD = 6i…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are find the cross product

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

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: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: Given points (-1, 5, 3), (3, -2, 4), and (-1, –3, 2). compute the area of the triangle they…

A: * A,B,C are points then unit vector is →AB×→ACII→AB×→ACIIand area oftringle is 12→IAB×→ACI

Q: Pls help

A: ABC is an equilateral triangle and D E f are the midpoints of the sides

Q: If u = 5i - j+ k, v =j - 5k, w = -15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)…

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Q: The angle that vector A =2ax+3a,+8az makes with x-axis is 56.14 42.03 76.82 68.19

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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: The points A, B, C and D form a parallelogram. The points A, B and C have position vectors 2i –…

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Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1:4, 3:2 and 3:7…

A: If the position vectors of A and Bare a→ and b→ then the position vector of point P divid.ing AB in…

Q: Consider the vectors ä = 5i+ 3- k, 6= 5i – 3 + k, 1+53+ 6k d = i+3+6k, j = -1-53+ k. Which pairs (if…

A:

Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1 : 4, 3 : 2 and 3…

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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: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

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Q: .If A = 2a, + a, - 3a, and B = 4ax + 2a, – 3a, are vectors, find (a) A· B (b) Á xB (c) Angle between…

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Q: The vectors A 6i + 4j – 8k and B = xi + 6j + zk are known to be parallel. Find x and z x = 9. -12

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Q: Given points P(4,2,-1), Q(2,-4,-1), T(4,3,4) forms the triangle. Find the unit vector that bisects…

A: We will first find the unit vectors along line QP & QT. So that the resultant vector which is…

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: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: Given the lengths of two vectors, namely, |u| = 1 and |v| =2, find the the dot product of u + v and…

A: answer is in next step.

Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using angles between located vectors,…

A: the given vertices are if the dot product of any two vectors is zero then we can say that A, B, and…

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: Q1.If à = 2a, + 2a, – a, and B = 3ax + 2a, – 6a, are vectors, find (a) Ả · B (b) Ả× B (c) Angle…

A:

Q: Find the measure of the angle between the two vectors. 4) u =(-6, -2) v = (6,-6)

A: An angle between 2 vectors is defined as, cosθ=u→·v→|u→||v→|   Here given vectors are,…

Q: Given the vectors, a = (4,-5) and b = -10i -8j: %3D a. Find a - 2b.

A:

Q: The angle that vector A=2ax+3a,+4az makes with x-axis is 68.19 56.14 76.82 42.03

A: We have to find the angle between vector A and X axis.

Q: Find the angle between the pair of vectors to the nearest tenth of a degree. (9, -1), (-4,-1) 79.8°…

A:

Q: Given vectors a, b, c, such that a = 5c + 3d and b = 2c -d, 2a -3b in terms of c and d. express

A: Given vectors, a= 5c+3d b= 2c-d

Q: - Find the lengths of triangle ABC using vectors, knowing that: A (3,1), B (6,4), C (-1,3)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Two vectors are equal is they are parallel and have the same magnitude and direction ylgn O ihi

A: For two vectors to be equal, they must have both the magnitude and the directions equal.

Q: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors .

A: A=4, 3, 0B=2, 3, 4C=5, 6, 2 REMEMBER A·B=ABCosθ⇒θ=Cos-1A·BAB

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: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors.

A: Dot product defined as  AB =|A| |B| cos x x is angle between A and B

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: 10,7 and -2,-75

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: Find the measures of the angles of the triangle whose vertices are A = * .(-1, 0), B = (2, 1), and C…

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Q: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: Find the measure of the angle between the two vectors. 24) u-(9,9) v-(-8,-5) V =

A:

Q: and b are two unit vectors such that + 2b and 5 a. 4 b are perpendicular to each other, then the…

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Q: Given the triangle with vertices A=(1,2,3), B=(3,-1,0), and C=(4,1,2), find unit vector of BM, i.e.…

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Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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Q: The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1 : 4, 3 : 2 and 3 :…

A:

Q: Given vectors: A(6,3,2), B(1,5,6) and C(6,2,0) forms a triangle. Find the length of the altitude of…

A:

Q: Show that each pair of vectors is perpendicular.     -6i -5j and 10 i -  12 j

A: If two vectors A and B are perpendicular then its dot product A.B=0Dot product:i, j,k are the…

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.