20. (i) Given the vectors a =i+ 4j + 2k, b = -2i + 2j + 6k andc = (a) The vector v, where v = a + b + c 3i – 3j – 2k. Find (b) The unit vector v (c) The angle, to the nearest degree, which v makes with the y axis |

Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: according to what you learned from the vector addition experiment, if we have vectors à = 2.4x – 3ŷ…

A: Given that,a→=2.4x⏞-3y⏞b→=4x⏞+5.5y⏞x⏞ and y⏞ are unit vectors representing positive x and y…

Q: 4 9. is 6/2 The distance between the vectors u = and y = -2 %3D -5 True O False

A: Suppose u and v be any vectors from a same vector space. Then the distance between u and v is…

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: 3. Given the vector ā = (x, y,=), where x = 0, y = 2 and z = 8 . Find the vector b with magnitude of…

A:

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

A:

Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: I reached this same conclusion " Tx=Ax1x2⇒Tx=0110x1x2⇒Tx=x2x1" but had difficulty explaining it in…

A: It can be proven that if x=x1x2∈ℝ2, then Tx=Ax=x2x1 where T is the linear transformation whose…

Q: 3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i+ j – k Answer + (2i+ 2.4j…

A:

Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

A:

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

A:

Q: Find a vector equation for the line through the point (-3, –1, 8) perpendicular to the vectors ū =…

A: Vector equation of the line passing through point (a,b,c) and perpendicular to vectors u→ and v→ is…

Q: solve for th e vector x in terms of the vectors a and b. x - a= 2(x - 2a)

A:

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

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Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

A:

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

A:

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

A:

Q: B) find a vector that is parallel to the line whose equation is : 4-x 3-6z % = 3 – 3y = 5 9

A:

Q: the component of vector a are ax=2.0 units and ay=3.0units while that of another vector b are Bx=…

A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

A:

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

A:

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is 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: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: Find the angle 0 between the vectors. 5T u-(cos , sin S), v-(cos, sin 4) = 4 4 3

A:

Q: b) Find the angle (0) between vectors between s = [1, –5, 4] and t = [3,3, 3].

A:

Q: 9. Which is traveling faster, a car whose velocity vector is 217 +35j or a car whose velocity vector…

A: We are authorised to solve only one question, please repost remaining questions Magnitude of vector

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: a) Find the vector that is parallel to the tanget to the circle x2 + y2 = 100 at the point (3,-4).…

A: a) Given equation of circle, x2 + y2 = 100. We have to find the vector equation which is parallel to…

Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

Q: 1. The two unit vectors parallel to the line y = 2x 1 are | and 2. The two unit vectors parallel to…

A:

Q: solve for th e vector x in terms of the vectors a and b. x + 2a - b = 3(x +a) - 2(2a - b)

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Q: The angle between the two vectors is not equal to Select one: O True O False u= and v= 0= π

A: Here we use the concept of dot product of the vectors.

Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: The relations between the unit vectors are ô, = ( sin 0 cos 4)ô, + ( sin 0 sin ø)ô, + ( cos 0)8, do…

A: We need to derive expressions A. 6-31, A.6-32, and A.6-33 by considering that A. 6-28, A.6-29, and…

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

A:

Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

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Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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Q: The distance between vectors v1 = (2, 1, -4) and v2 = (1, -1, -2) equals: Select one: O a. -2 O b. 3…

A: To find The distance between the two vectors v1=(2,1,-4) and v2=(1,-1,-2)

Q: The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y)…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.