3. Find the angles a, ß,y, which the vector Á = 3î – 6î + 2k makes with the coordinates axes and also show that cos?a + cos²ß + cos²y = 1. %3|

Q: Find the component form of the sum of u and v with direction angles ey and Oy. Magnitude Angle ||-||…

A: The x, y  coordinates of the vector are given as rcosθ and rsinθ respectively. The component form is…

Q: 4) Given a = 2i + 3j + k , b = 3i – Sj + 9k and c the vector joining P1 (3, 4, 5) to Pz (1, -2, 3) ,…

A: The vector C is:  c→=1,-2,3-3,4,5    =-2,-6,-2

Q: Given vectors u and v in the diagram below, shade in all linear combinations cu + dv for (a) -1 1…

A: (a) Shade the linear combination.

Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectangular coordinate system (x,y,z) SCS- Spherical coordinate system ρ,θ,ϕ CCS- Cylindrical…

Q: Find the direction cosines of u and demonstrate that the sum of the squares of the direction cosines…

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Q: Suppose the vector t has magnitude 34 and makes an angle of 200° with the positive x-axis (measured…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Given: The magnitude and direction of two vectors  u=9, θu=0°v=2, θv=60° To find the component form…

Q: Given the vectors v 4i + 2j - 3k and w = 3i – 4j + k.. Find the angle between v and w.

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Q: Suppose the vector s has magnitude 86 and makes an angle of 147° with the positive x-axis (measured…

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Q: Find U+W and V Angle between WHi-; U= 3i+4j

A:

Q: Given vector a = 31 – 2j – yk and b= 3i- 2j + k. What is the value of y if a =b

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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: nd the direction cosines of u and demonstrate that the sum of the squares of the direction cosines…

A: Sum of square of direction cosine is equal to 1

Q: 5. For the vector OP = (1,4,-2), determine the direction cosine and the corresponding direction…

A:

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: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A:

Q: Suppose that v and w are unit vectors. If the angle between v and i is a and the angle between w and…

A: Vector is a physical quantity having both magnitude and direction . Dot product of two vector A and…

Q: 4 3 Let U 4 and V = - 5 - 3 -2. Find the angle between the vectors (in radians).

A:

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: topic - vectors

Q: Suppose the vector t has magnitude 21 and makes an angle of 228° with the positive x-axis (measured…

A: Given,  Magnitude=21, angle=228°   Recall:  Formula:     a=(magnitude)(cos(angle)),…

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: I am attaching image so that you understand each and every step.

Q: s given 2 vector A and B of non zero magnitude, what is the angle between them if A.B as value -AB/2

A: The dot product between two vectors, X and Y is defined by the formula, X·Y=XYcosθ, where, θ is the…

Q: . Find the angle between the vectors å = 4i – 35 + k and b = 21 – k. (First find an exact expression…

A:

Q: Given the vectors u=(5,8) and w =(-4a,5a+5), where a is a constant. If it is known that u' +w°…

A: u→=5,8w→=(-4a,5a+5)

Q: Find the component form of u + v given the lengths of u and V and the angles that u and v make with…

A:

Q: Q3) If A -3i + 4J – 5k and B= 5i-6J +7k find the unit vector which is perpendicular to these two…

A:

Q: The vector êr and êe in terms of î and ĵ is given by êr = î cos e + ĵ sin 0, %3D and êe = -î sin 0 +…

A: True

Q: =5, and the angle between u and v is 30°. Find the magnitude (to onc decimal place) and direction…

A: Given that: |u→|=2 and |v→|=5 and angle between u→ and v→=30°

Q: Suppose the vector t has magnitude 64 and makes an angle of 243° with the positive x-axis (measured…

A:

Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle e between the vectors v and w.…

A:

Q: 4) Given a = 2i + 3j + k , b = 3i – 5j + 9k and c the vector joining p1 (3, 4, 5) to P2 (1, -2, 3) ,…

A: Given,  a→=2i^+3j^+k^ Also given c→ is the joining vector of p13,4,5 and p21,-2,3 Then,…

Q: Find the angle between u=3i+2j and v=-4i

A: Given,          The two vectors are u=3i+2j and v=-4i.

Q: ) If m = 2i+2j-k and n = 31-6j+2k, find: a) m ·n and b) the angle between m and n. c) the component…

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Q: Suppose the vector s has magnitude 73 and makes an angle of 114° with the positive x-axis (measured…

A: Answer

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Given that, ‖u‖=2,  θu=5‖v‖=1,  θv=2 The objective is to find the component form of  u+v.

Q: Question 17 Let A and B be points with position vectors u and v such that [u] = 6, |v| = 8 and u v=…

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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 component form of u + v given the lengths of u and v and the angles that u and v make with…

A:

Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

A:

Q: Part 1: Given the vector B = pz sin o a, + 3pz² cos o as +º az and point F(3," rad, 2), determine…

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Q: In the diagram below, a and b are vectors such thay cos0 = 1/6. Given thay a= i +j+ pk and b= 2i…

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Q: Find the angles that vector D 2.5 - 8.5 + k) m makes with the x-, y-, and z- axes.

A: Follow the procedure given below.

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A:

Q: Given the vectors v = 4i + 2j + k and w = 3i – 4j + k. Find the angle between v and w .

A: We know, the angle between two vectors v→ and w→ is θ = cos-1v→·w→|v→| |w→|

Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: Determine the Vector equation: Convert spherical ρ,θ,ϕ to rectangle x,y,z coordinates by…

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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Q: Let a = (4, 1) and b (4, – 1). %D | Find the angle between the vector, in degrees.

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Q: 4) If p = 6i+7j-2k and q = 31-j+4k, find: a) p x q b) the sine of the angle between vector p & q. c)…

A: