Let v be the vector The vector of length 3 in the opposite direction as v is 2 Select one: a. -2 O b. V3 O C.

Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: find the given vector  Unit vector ew where w = (24, 7)

A: Given: w=24,7

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = −(1/4)i + (3/2)…

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Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: Find the component form of the vector.The vector PQ , where P = (1, 3) and Q = (2, -1)

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Q: Find the vector v with length 2 and the same direction asthe vector u =(=6,5,3). a) 12 10 b) 12 10…

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Q: Find the unit vector having the same direction as v. v = 3i + - 4j O A. u= 15i + - 20j OB. u- - 5 B.…

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Q: For what value of t, if any, is the vector (8t, 2) parallel to the vector (4, -1) ?

A: Given vectors:A= <8t, 2> and  B= <4, -1>

Q: If a = i+ 4j + k and b =i+ 8j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: For AABC, let b and c denote the vector AB and AC , respectively. The vector BH is orthogonal to AC.…

A: Orthonormal vectors are perpendicular to each other.

Q: H For the pair of vectors u = and v = in R*, find the size of the angle 0 between u and v. Hence,…

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Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

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Q: a. Find a vector and unit vector perpendicular to each of the vector à + B and à – Ē , where à = ai…

A: Given: Vectors are A→=ai+4j+bk and B→=6k+i+2j To find: A vector and unit vector perpendicular to…

Q: Rewrite the following vectors in term of unit vectors а. ОP %3D (9, -2) b. 0Q = (7,0,8)

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Q: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

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Q: For what value of t,if any, is the vector (1, 4t) parallel to the vector (4, - 1)? Not OA. t = -2…

A: If the Vectors u and v are parallel then u=kV , K is any scalar.

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: Given: f(x, y) = 3x² – 2y² at (-,0) in the direction from P(-,0) to Q(0,1). . What is the unit…

A: The given problem is to find unit vector of the function in which direction from point P(-3/4,0) to…

Q: Consider the vector w = n ^ (v ^ n) where n is a unit vector, and v an arbitrary vector. What are…

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Q: Find the unit vector u in the direction of the vector v=2( 3, 0, 4 ). 1 u = V O A. 15 1 OB. 25 1 U =…

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Q: Let v be a nonzero vector. If 0 is the direction angle measured from the positive x-axis to v, then…

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Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

Q: Find the x-component of this vector: 47.3 m 39.4° Remember, angles are measured from the +x axis.…

A: To find:- x and y components of given vector in figure

Q: Find the direction of the resultant vector. (8, 10) V (7,-1) W [?]° 1>13

A: The given data is: v→=8i+10jw→=7i-j  To find the direction of the resultant vector.

Q: 2. Given the figure below, find a single vector that is equivalent to D B a) E-A tw IA tu F to G

A: given vector bundle

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

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Q: Find a vector that is perpendicular to both and 2. A =-i - 2j +4k B = 4i - j

A: Take cross product and it's magnitude then find unit vector in perpendicular to both vector

Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

Q: Express the following vector as a product of its length and direction: v = 4i + 8j – 16k -

A: Given vector is v→=4i+8j−16k. We have to express the given vector as a product of its length and…

Q: If a = i+ 10j + k and b = i+ 11j+ k, find a unit vector with positive first coordinate orthogonal to…

A: Vector cross product of given two vector  is orthogonal to two given vector

Q: Express the following vectors in Cartesian (component) form. a) f has magnitude 20 and direction…

A: Solution:-

Q: If a = i+ 8j + k and b = i+ 13j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Let v be the vector . The vector of length 5 in the opposite direction as v is Select one: a. 5 -5…

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Q: Find a vector and unit vector perpendicular to each of the vector à + B and à – B , where à = ai +…

A: We have A→=ai+4j+bk  and B→=6k+i+2j Here a=0 and b=5 So, we have  A→=0i+4j+5k  and B→=i+2j+6k Now,…

Q: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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Q: For any nonzero vector v, the unit vector that has the same direction as v is________ . To find this…

A: For any nonzero vector v, the unit vector that has the same direction as v: To find this vector,…

Q: Find the value of a in the vector i = (a, b) if b = 48 and ||ū|| = 50 %3D v is in Quadrant I

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Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Given the vector u= find |ū| and the direction of ủ.

A: We have the vector u→=-3,8. Then we have to find u→ and the direction of u→.

Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

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Q: If a = i+ 3j + k and b = i+9j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: 2. Given the figure below, find a single vector that is equivalent to C B tw b) 10 14 וד --(A-F+C) G…

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Q: Let v=5i+2j. Find a vector that is twice the length and points in the opposite direction as v.

A: This is a problem related to vector. Based on the general formula and concept we will answer the…

Q: Which of the following planes are parallel to the vector (4, 1,-5)? Select one or more: O a. 6x + y…

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Q: (d) Explain why each vector VER can be expressed in precisely one way as v u+w, where u ES and w ES.

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Q: find the component form of the vector. The vector PQ, where P = (1, 3) and Q = (2, -1)

A: The component form of a vector XY with X=x1,y1 and Y=x2,y2 is defined as follows: <x2-x1,…

Q: If a = i+ 4j + k and b = i + 8j + k, find a unit vector with positive first coordinate orthogonal to…

A: Given : a=i+4j+k and b=i+8j+k.

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.