Suppose that v and w are unit vectors. If the angle between v and i is a and that between w and i is B, use the idea of the dot product v•w to prove that cos(a B) = cos a cos B + sin a sin ß -

Q: 1. Find the angle between the following two vectors. and

A: The given vectors,  8,-5 and -9,-7

Q: Given vectors u=i+2j and v = 3i + yj, find y so that the angle between the vectors is 60°. roo…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 14i V=-7i

A: To find Angle between two vector a→,b→ we use, cos α =  a→·b→|a→|·|b→|

Q: Find the angles between the vectors to the nearesthundredth of a radian. u = 2i + j, v = i + 2j - k

A: Now,

Q: Given the cross product of 2 vectors u and v is, u × v = −3i + 2j – k, and their dot product is, u ·…

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Q: Suppose that U and V are vectors of lengths 2 and 3, respectively. If the angle between U and V is…

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Q: Find the angles between the vectors to the nearesthundredth of a radian. u = 2i - 2j + k, v = 3i +…

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Q: When the angle between vectors u and v is between 0° and 90°: || You can't tell O t • 0

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Q: Find the angle between the vectors in degree and in radians ) i + sin ()j, v = cos E) i+ sin 37 +…

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Q: If θ is the angle between two nonzero vectors u and v, then cos θ = ________.

A: If θ is the angle between two nonzero vectors u and v, then    cos (θ) = (u.v)/(||u|| ||v||)

Q: If F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis…

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Q: Find the angle u between the given vectors to the nearest tenth of a degree.    U= 13i, V = 26j

A: Consider the given: U=13iV=26jU⋅V=13i⋅26j=130+026=0

Q: Given 2 non-zero vectors ū and v, calculate (4ü +3v)•(2ũ – v) and express the final answer in terms…

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Q: If v × w =4i −j +k, and v⋅w=5, and θ is the angle between v and w, then tanθ = ? v and w are…

A: Given  v × w =4i −j +k, and v⋅w=5, and θ is the angle between v and w  Now we have to find tanθ as…

Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

Q: Given vector a= i+ 2j and b= 2i + 5j. Let 0 be the angle between the vector's directions. Compute…

A: Consider the given vector a→=i+2jb→=2i+5j   Find the magnitude. a→=12+22=1+4=5   b→=22+52=4+25=29

Q: The angle 0, 0 SOST, between two nonzero vectors u and v can be found using which of the following…

A: Answer:(d) cos θ=u.v|u||v|

Q: Let the cosine of the angle between the vectors p and q be à such that 2p + q = i + j and p + 2q =…

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Q: 3. Given the vectors v = i- 2j – 2k and w = 31 – 5j + 4k, find (a) the cosine of the angle between i…

A: The given vectors are, v→=i-2j-2kw→=3i-5j+4k The magnitudes of the vectors are as,…

Q: Suppose the vector w has magnitude 16 and makes an angle of 339° with the positive x-axis (measured…

A: Given:    Magnitude ( r) = 16    Angle = 339°

Q: Find the given vector : Unit vector e making an angle of 4π/7 with the x-axis

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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 e (in radians) between the vectors. co()i - sin(); u = cos 4 v = cos i + sin 4 4 e =…

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Q: 20. By forming the cross product of two appropriate vectors, derive the trigonometric identity sin…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 15i – 6j, V = 4i +…

A: Given, Vector U = 15i -6j        U = 152 +(-6)2 = 225+36 = 261 = 16.2 Vector V = 4i +13j         V =…

Q: The angle between the vectors i + 2j + k and 3i+ j - 5k is

A: Given: Let, A=i+2j+kB=3i+j−5k

Q: Suppose that u and v are unit vectors in R°. If the angle between u and v is T/4, then what is the…

A: Given that vectors u and v are unit vectors and angle between vectors u and v is π4.  We know that…

Q: What is the angle e between the vectors u= and v= in R* ? (Express the answer to the nearest…

A: B

Q: If the two vectors are in the following figure, find the angle (1) between them A=i+j-k B=2i-2j+2k

A: Given

Q: 1. To the nearest tenth, find the angle between the two vectors below. v = 3i – 2j w = 2i + 2j

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Q: Find the angle between the given vectors. Round to the nearest tenth of a degree. u = i - j, v = 3i…

A: Here we will find the angle between given vectors,

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 14i + 6j, V = -13i…

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Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: Find the angles between the vectors to the nearesthundredth of a radian. u = √3i - 7j, v = √3i + j -…

A: Given:u=3i-7jv=3i+j-2kAngle:cosθ=u→.v→u→.v→

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

A: Given Data: Vector 1: x1i+x2j+x3k=4i+2j-3k Vector 2: y1i+y2j+y3k=mi-j+3k The magnitude of vector 1…

Q: Find the angle between the given vectors to the nearest tenth of a degree. U = 13i - 4j, V = 2i +…

A: For two vectors a and b we know that their do product is a·b=abcosθthen cosθ=a·bab…

Q: Consider two vectors u, v, and is the angle between them, which of the following is false A. 00 if…

A: Given two vectors u→,v→ and θ is the angle between them

Q: Given these vectors find the sum of U+V (Question in the provided attached photo)

A: Given these vectors find the sum of u+v.    u=-4,-4 and v=1,8

Q: Q2/ what the sine of the angle between the vector d= 3î + ĵ + 2k , b= 2î – 2j + 4k -

A: Here given vector as a=3i+j+2k, b=2i-2j+4k Thus a=32+1+22=9+1+4=14 a=22+-22+42=4+4+16=24=26

Q: Find the angle 0 between the vectors. (c0 ST, sin S), v- (cos , sin ) 5Tt 4 COS 3 COS 4 radians

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Q: For vectors ū = (1,-5,2) and v = (3, 1,-4), calculate the following: a) ū• i b) the angle between ū…

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Q: and D. Find the values of x such that the angle between the vectors is 90".

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Q: In many applications, the angle 0 between vectors play an important role; usually in the form of…

A: We will find out the required value.

Q: Given the following vectors: di = 3î – 2j, d, = -5î + 2j – k What is (di + dz) · (dị × (4dz))?

A: d1 =3i-2j+0k d2 =-5i+2j-k

Q: 2. Find the angle between the following two vectors. and

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Q: Given that the angle between the vectors a and b is n/3, then the angle between the vectors -a and b…

A: Angle between two vectors a and b is π3 Let us find the angle between -a & b  Represented in a…

Q: and Let ū Let e be the angle between ū and ū. ob tuse ? why ? acute, right , or ca) Is (6) Find a…

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Q: If v · w is negative, what does this say about the angle between v and w? Draw a 3-dimensional…

A: we have been given that v.w is negative which means v · w < 0 which means the angle between v and…

Q: The vectors i = (-4, p, –2) and j = (-2,3, 6) are such that the angle 0 between them satisfy…

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