Let the angle between two nonzero vectors u and V be 45°, the magnitude of the vectors be a and 2 respectively, and the dot product be 4V2. Then which of the following is the value of a ? (a) 4 (b) 3 (c) 2 (d) (e) V3

Q: Find the angle, to the nearest degree, between the vectors U and V U=4i+5j, V=7i−4j

A: Consider the given vectors U=4i+5j , V=7i-4j First, find the dot product of vectors of U and  V…

Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: 5. D The angle between two vectors a and b is -, Given that /a/ = 3 and /b/ = 4. find (a) /2a + 3b/…

A: Vectors

Q: B. For vectors u = and v = Find 1. 4u – 2v 2. A vector of length 20 in opposite direction of 4u – 2v

A: For the vectors u = ( 2, 0, -3 ) and v = ( 0, 1, -2 ) we need to answer the following questions.

Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when

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Q: Find the magnitude of the vector and the angle 6,0° <0<360°, that the vector makes with the positive…

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Q: Find the positive value of m that makes the angle between the vectors equal to 5 a = i +j+k b = mi –…

A: Given that, a⇀=i^+j^+k^ b⇀=mi^-k^ Then we get, a⇀·b⇀=i^+j^+k^·mi^-k^a⇀·b⇀=m+0-1=m-1 Moreover we get,…

Q: Q2: Find the angle between the vectors à and b where a = i+ 2j – k and b = -i+j-2k.

A: The angle between two vectors A→ and B→ is calculated as, cosθ=A→.B→AB The given vectors are,…

Q: 6. Find the magnitude of the resultant of two vectors u and v, given u=2, y =7 and the angle between…

A: We have to find the magnitude of the resultant of two vectors and v and the angle between the…

Q: In a triangle ABC, points E and F are on the sides AC and BC respectively, such that AE is 1/3 of AC…

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Q: (3) For what value(s) of a will the vectors u = 2i + 4j-5k and v= -4i-8j + ak be parallel? V ا ) وہ…

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Q: a/The angle between the two vectors A2 Bz 3 TT 2

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Q: Suppose that the magnitude of vector u = 5 and the magnitude of vector v=7 and the dot product of u…

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Q: 3. Given the following vectors, find their sum, difference, dot produet and cross product. A- 2£ +…

A: All parts of Question 3 is solved.

Q: Q2: Find the angle between the two vectors A = 5i - j+ 2k and B = -3i + 2j + k

A: Angle between the vector u and v is θ=cos-1u.vu.v.

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 12i + 6j, V = -13i…

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Q: Find the angle between the vectors v and w v = (2, 1, 3)T , w = (6, 3, 9)T

A: We need to find the angle between the two vectors.

Q: Find the angle between the vectors v and w v = (2,−3)T , w = (3, 2)T

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Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: 4. Find the angle between each pair of vectors. Round to two decimal places as necessary. a) (V3,…

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Q: Find the angle between the vectors r = (-1, 2) and s = (4, 2)

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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: Find the angle between the given vectors to the nearest tenth of a degree.u = &lt;2, -4&gt;, v =…

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Q: Given the two vectors A = 3ix + 4iy and B = 7ix – 24 iy a. What is their dot product? b. What is…

A: Given : A=3ix+4iy, B=7ix-24iy.

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

A: Given: 6j, -4i

Q: Find the angle between the vectors u = i − 2j + 2k and v = −3i + 6j + 2k.

A: In this question we have to find the angle between the vector.

Q: Find u * v if u and v are unit vectors and the angle between them is (2pi)/3

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Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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Q: Q3: Find the angle between two vectors in space A = 41 – 2J – k and B = 4T – 2J + 4k (5 marks)

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Q: The angle between the vectors a=(2,6) and b=(3,-1) is :إختر أحد الخيارات а. 4 b. С. 3 d. 2

A: The required angle is, option (b) π/2 The detailed solution is as follows below:

Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when |-5V3A x B = 5Ã.B

A: To find the angle θ between vectors A and B. It is given that,

Q: .Let u and v be two vectors with u x= 2 and 7-5=-2 Find the angle 0 between u and i

A: cross product of the vectors:A⇀×B ⇀= A⇀B⇀sinθn^  (It's a vector quantity.)A⇀×B ⇀ =  A⇀B⇀sinθDot…

Q: 2. For the vectors (1, 1) and =(-1,1) Find the dot product u · v, and the angle 0 between the two…

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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: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

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: Let the angle between two nonzero vectors u and V be 30°, the magnitude of the vectors be 3 and x…

A: Solution-

Q: 10î - 4ĵ +7 k̂ and B =

A: Find the dot product A∙ B and its angle of the given vectors: A = 10î - 4ĵ +7 k̂ and B = -2î +ĵ +…

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: The problem refers to a vector V with magnitude |V| that forms an angle with the positive x-axis.…

A: Answer is provided below

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

A: a) If u and v are two-dimensional vectors, we calculate the dot product as   u=(u, u2) and v=(v1,…

Q: For what value of "c" are the following vectors perpendicular? 3 (2, с, 9) аnd ў 3 (Зс, —1,5) (Зс, —…

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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 direction angles of the vector. V = -3i + 2j - 4k

A: The given vector is v=-3i+2j-4k

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

A: