Show that the vectors 3 do not span R° by giving a vector not in their span.

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

Q: onow that the v ectors 2 3 do not span R' by giving a vector not in their span.

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Q: Determine the two unit vectors that are orthogonal to v = (1,2). Which two unit vectors are parallel…

A: Let the required unit vector orthogonal to v be <x,y>

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: If vector a= and vector b= are vectors a and b orthogonal, parallel, or neither? Provide

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Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

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: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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Q: Let b be the vector of length 35 that when drawn in standard position makes a 290° angle with the…

A: Given : length of vector b=35 ⇒b=35 Also, b makes angle 290° with positive x axis. So, b=b1i+b2j,…

Q: Find a vector that is oppositely directed to v = with a length of 4

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Q: The vectors į+j and i-į are perpendicular. True False

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Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: The vectors and are parallel. True False

A: Recall: ⇒ Two vectors are parallel if one is a scalar multiple of the other.         i.e, Let a→ and…

Q: Which of the following vectors are parallel :

A: Two vectors are parallel if one can written as linear combination of other.  As showing in the hand…

Q: latél Show that if a is perpendicular to each of the vectors and then a is perpendicular to 26 +4

A: The detail solution is given below

Q: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

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Q: Find all unit vectors perpendicular to (3,1,4) that make equal angles with j and k.

A: Here we have to find the all unit vectors perpendicular to (3,1,4) that make equal angles with j and…

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Find the angle a between the vectors 5 2 and 1 a =

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Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: Two nonzero vectors are perpendicular if and only if their _____ _______ is equal to______.

A: Given:Two nonzero vectors are perpendicular if and only if their ______is equal to ______

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: Find two independent vectors both of which are perpendicular to i = 3

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Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: Show that the vectors do not span R' by giving a vector not in their span.

A: Solution :-

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Suppose that u and v are vectors in R' both of length 2V2 v is also? v2. Thenllu + v|| and that the…

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Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: Find a vector that is oppositely directed to v = with a length of V3

A: We have to find the vector by given data

Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.

A: We have to show that if A ⋅ (B × C) = 0 then all three vectors A , B , and C lies in the same plane.…

Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

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Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

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

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Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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Q: value

A: If, P, Q & R are collinear, then,  The position vector of QP is, The position vector of P - the…