If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of the three vectors i, j, or k. اختر احدى الدجابات True False

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

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Q: 4. Find a unit vector that is perpendicular to (5,6).

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Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

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

A: See the attachment

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

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Q: 2 Find the angle between two vectors Ā - Hax-Gay -89z B-Gax + 10ay + Saz

A: Angle between two vectors A⇀ and B⇀ is θ=cos-1A⇀·B⇀A⇀B⇀

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: is The unit vector in the direction of v=(4,0,–3)

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Q: Given a position vector v, why are there infinitely many vectors equal to v?

A: For given position vector, there are infinitely many translations possible. It is known that the…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

Q: Which two vectors are perpendicular to both a and b?

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Q: Find the angle θ between the two vectors.u = (0, 4, 0, −1), v = (1, 1, 3, −3)

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Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u3(-12,0,6)…

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: Find the length of the vector. v = (0, 9)

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Q: Find a unit vector that is orthogonal to both u and = (-8, -6, 4) v = (17, -18, -1)

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

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 between the vectors u and v if u = (2,3,5) and v = = (1,–4,3) in

A: First we convert this into vector then find the angle

Q: Compute |u × v| if u and v are unit vectors and the angle between them is π/4.

A: u and v are unit vectors and angle between them is π4

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: Find the angle θ between the two vectors.u = (10, −5, 15), v = (−2, 1, −3)

A: The given vectors are To find the angle between the given vectors, use the formula

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: Compute u v if u and v are unit vectors and the angle between them is

A: topic- dot product of vectors

Q: For the vectors u = (- 3,5) and v = (- 5,2), calculate proj,u and scal,u.

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: Find the angle between the vectors u (2, –1) and v = (1, 1).

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Q: Find the angle between the vectors u = (2, 5) amd v =

A: Given: There are two vectors: u=2,5v=4,-3 To determine: The angle between the given two vectors.…

Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: Find the angle between the vectors. a=(3, 4, – 2), b=(0,1,2)

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Q: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: Find a unit vector that has the same direction as the given vector. (-8, 8, 4)

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Q: Find the angle θ between the vectors.u = (3, 1), v = (−2, 4)

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Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

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Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: Find a unit vector that is orthogonal to both u and v.      u = ⟨−8, −6, 4⟩,          v = ⟨10, −12,…

A: Consider the following vectors: u=-8,-6,4v=10,-12,-2 A vector orthogonal to both u and v is the…

Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors

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: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

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Q: Find the unit vector that has the same direction as vector v that begins at (0, -3) and ends at (4,…

A: If a vector is of the form ai^+bj^   then its unit vector along the direction v is written as…

Q: Find the angle between the vectors u and v if u (2,3,5) and v = : (1,–4,3) in (Ctrl) ►

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Q: Find a unit vector u that had the same directions as the vector v= (-3,3,-2)

A: Use the basic property of unit vector

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

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find a unit vector that has the same direction as the given vector. ‹-3, 3, 4›

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Q: 4. Find a unit vector that is perpendicular (5, 6). to

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