Point A(-4, 2, 5) and the two vectors, RAM = (20, 18 – 10) and RAN = (-10, 8, 15), define a triangle. Find (a) a unit vector perpendicular to the triangle; (b) a unit vector in the plane of the triangle and perpendicular tc RAN; (c) a unit vector in the plane of the triangle that bisects the interior angle at A.

Q: A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29° and 53⁰ with…

A: This question can be solved using the concept of vectors.

Q: or what values of aj are the vectors [ai,4,3] and a) orthogonal? b) Parallel? c) Have 45 degree…

A: If 2 vectors a⇀,b⇀  are orthogonal, their dot product a⇀.b⇀ =0 Let u=a1,4,3 and v= 3,-2,12 So,…

Q: In Cartesian coordinates, the position vector at point (3, 40, 1) is represented by

A:

Q: Write three properties of parallel vectors p and q.

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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: Determine the two unit vectors that are orthogonal to v = (1,2). Which two unit vectors are parallel…

A: Let the required unit vector orthogonal to v be <x,y>

Q: What unit vector is in the same direction as v = 2i - 4j?

A: The unit vector in the direction of vector V is given as:

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Q: What is the unit vector in the direction of v = ?

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Q: A parallelogram is determined by the vectors = (-2, 5) and 7= (3, 2). Determine the angle between…

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Q: If two nonzero vectors are perpendicular, then the angle between them is 90°. Also, the cosine of…

A: Given ,  If two nonzero vectors are perpendicular, then the angle between them is 90°. Also, the…

Q: Show that vectors a = (4,0, – 1), b = (1,3, 4), and c = (-5,–3,–3) form the sides of a triangle. Is…

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Q: Find the sum of the given vectors. a - (3, 0, 2), b- (0, 6, 0) Illustrate geometrically.

A: Given, Two vectors  a = ⟨3, 0, 2⟩   b = ⟨0, 6, 0⟩  We have to find the sum of vectors and illustrate…

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: Write the vector v = ⟨2, -4, 4⟩ as a product of its magnitude and a unit vector with the same…

A: Given vector is  v=2,-4,4 Magnitude of vector v  is v=(2)2+(-4)2+(4)2=4+16+16=36=6 Now, unit vector…

Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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Q: Find the angle between two vectors by using cross product (V,xV2) V, = 3i + 9j + 6k V2 = i + 3j + 2k…

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Q: prove using vectors that the points (0),2 -2- (B2,0, -2, C, (2,2-,10) represent the vertices of a…

A: We have to check weather the given points are Vertices of Traingle or not.  After that we have to…

Q: A triangle is formed by the vectors (4,1) (1,3) and (3,3). Determine the area of the rectangle,…

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

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

A: Find the solution below

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

A: a) Given: v1=<-3,6>,…

Q: Given a vector with initial point (−8, 3) and terminal point (5, −5), find an equivalent vector…

A: In the question we have to find an equivalent vector with initial points (0,0).

Q: A figure is translated using the vector (-3, 7). What translation vector would move the image back…

A: i have provided solution in step2

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: find the angle between vector A = and vector B = then write A as a sum of a vector parallel to B…

A:

Q: (6, -2, -4), and the unit vector from the origin toward point B is (2, -2, 1)/3. If points A and B…

A: The vector from the origin to point A is given as (6, −2, −4), and the unit vector directed from the…

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

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

A: Consider the graph

Q: 3. State the components of a unit vector that is perpendicular to the vector =(5,2,-1).

A: To state the components of a unit vector that is perpendicular to the below vector v. v=5, 2, −1

Q: Find a unit vector in the direction of

A: Given that,   vector = <6, 3, 2> = u¯ (Say)   Unit vector = u¯u = <6,3,2>62+32+22 =…

Q: Point A(-4, 2, 5) and the two vectors, RAM = (20, 18-10) and RAN = (-10, 8, 15), define a triangle…

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Q: Determine the area of the parallelogram determined by the vectors ⟨5, 3 ⟩ and ⟨−8, −1 ⟩. Determine…

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Q: 1) Given two vectors as A = 2â, + 2â, -â, at point (3,60°,180°) and B =-2â, + 4â, - 4â, at point…

A: Consider the given vectors:

Q: Find the angle between the vectors. a=(3, 4, – 2), b=(0,1,2)

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Q: Find the angle between the vectors i [- 9,1, 3] and i [0,2, – 5]. %3D

A: here we have to find the angle between the two vectors. the soltion is following.

Q: Find the angle θ between the vectors.u = (3, 4), v = (5, −12), ⟨u, v⟩ = u ∙ v

A: Given vector: Formula used : By dot product equation:

Q: A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29° and 53° with…

A: We have to find tension in cable.

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

A:

Q: 4. Point A (-4, 2, 5) and the two vectors, RAM = (20,18, – 10) and RAN = (-10,8, 15), define a…

A: We have to find unit vector perpendicular to triangle and according to given question.

Q: Two vectors with forces of 96 newtons and 74 newtons act at a point. Use the parallelogram rule to…

A: Explanation of the answer is as follows

Q: Find the angle 6 between the vectors. u- (1, 1, 1), v- (5, -4, 3), radians

A: Angle between the two vectors can be found by applying dot product of two vectors.

Q: Please state the Pythagorean Theorem using the language of vectors; then prove it.

A: In this given question ask state of pythagorean theorem using the language of vectors and prove it.…

Q: Find the vector in v that has magnitude 8 and is in the opposite direction of (-3, –5, 1). v = help…

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Q: ū = (-2, -12, 4), ₺ = (3, -2, 1).

A: Here we use the vector addition formula.

Q: Find the area of the parallelogram that has the vectors u (2,-1, 3) and v (4, -5, 1) as adjacent…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

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: Use the vectors vec{u}=(1,-2,5)  and vec{v}=(0,-1,3) to Find, vec{v} - (2vec{u})  and the unit…

A: topic - vectors

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

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