Given the vectors u=(5,8) and w =(-4a,5a+5), where a is a constant. If it is known that u' +w° =(-15,38), the measure of the angle e formed between u' and w corresponds to: 5 a) 0 = cos™ /3600 105 b) 0 = cos /231400 140 c) 0 = cos /115700 1845 d) 0 = cos 1594346

Q: Find three mutually orthogonal unit vectors in R° besides +i, ±j, and tk. 3

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Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: If the volume of the parallelepiped determined by the vectors A = i +ak, B = 8i-5j + ak and C = 2i…

A: Given vectors are A = i + αkB = 8i - 5j + αkC = 2i + 3j - 8k

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Suppose that u and v are vectors in R' both of length 2/2 and that the length of u – v is also2 /2.…

A: The solution is give as

Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

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: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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Q: find the given vector  Vector v of length 2 making an angle of 30◦ with the x-axis

A: To find: the vector v of length 2 making an angle of 30◦ with the x-axis

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: The angle between two unit vectors e and f is π/6 . What is the length of e × f?

A: The angle between two unit vectors e and f is π6.

Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

A:

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

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: What is the angle measure between the vectors u = (-5, 8) and v = (3, 9)?

A:

Q: If the volume of the parallelepiped determined by the vectors A = i + ak, B = 8i - 5j + ak and C =…

A:

Q: Consider two forces of equal magnitude acting on a point. When the resultant of the forces is 0,…

A: given: the two forces of equal magnitude acting on a point and the resultant of the forces is 0.

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (2, 5, 3), Q = (– 3, –…

A:

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

A:

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 v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

A:

Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

A:

Q: The inner(dot) product of two vectors and with lengths a and b. is given by a-b = abcos(y+2 T) ,…

A: The statement is true. The given statement is true because , Given a→.b→=abcosγ+2π But, cos…

Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

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Q: A=\+2) -Kg B=-i+j+ K, Csitk, D= i+2j-K which vectors are: @ perpendicular parallel-

A:

Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

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Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: After decompsing the Veclor A-2i-j+3k to Hhe Sum of tado vectors, the first is Parallel to the…

A: Every vector can be decomposed into two vectors. One vector is parallel to another given vector, and…

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

A: Area of the prallelogram using cross product

Q: Suppose that u and v are vectors in R' both of length 2V2 v is also? v2. Thenllu + v|| and that the…

A:

Q: The vector from the origin to point A is given as 6ax – 2a, – 4az, and the unit vector directed from…

A: Given vector is A→=6,−2,−4 and B→=B23,−23,13 And B−A=10 We have to find the coordinates of the point…

Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

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Q: The angle between the vectors ū = i + 2j – 4k and w = 2î + 3j + 5k is obtuse.

A:

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: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

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Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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Q: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

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Q: Which polygon is the result of reflecting polygon 1 through AB, then translating the reflected…

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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: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

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

A:

Q: Two out-of-phase alternating voltages are represented by: = 3.4sin (wt +) and V, = 1.3cos (wt +).…

A: we will find horizontal and vertical component of each voltage and then represent them in vector…