Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which valuc of x are v =< 1,3, 5 > and w =< 3, x, –1> orthogonal?

Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

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

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Q: Find the angle mesure between the two vectors u and v where : u=-2i + 2j + 4k, v=3i + 8j + 2k write…

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Q: snip

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Q: Find the area of the parallelogram determined by the vectors u and v.

A: Given any non-zero vectors.

Q: (A) Find the vector that is Normal to: A = 2i + 3j +k and such that it is lies in the plane…

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Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

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Q: find the acute angle between the given linesby using vectors parallel to the lines. y = x, y = 2x +…

A: Here the acute angle between two lines is to be calculated.

Q: Find the angle e between the vectors. f(x) = 2x, 9(x) = 4x2, (f, 9) = radians

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Q: Express the vector in terms of the unit vectors i and j. 4) (4,

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Q: Find the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: A vector of 2 unit length parallel to vector 2i + 2j+k is:

A: We know a vector consists of magnitude and direction as we have to find the direction parallel to…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: Prove the stated property of distance between vectors. d(u, w) &lt;= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

Q: Use the cross product u ✕ v to find the obtuse angle between vectors u and v, where u = −i + 6j +…

A: The answer is in step 2.

Q: What is the area of the parallelogram formed by the vectors v = (1,0, 1) and w = (0, 2, 2) tail to…

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Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: products

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Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: Find the cross product of the unit vectors. jx i

A: Topic :- Vector

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a…

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Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: For the vectors u=i+6j+2k and v = 2i - 2j + 5k, calculate projyu and scal, u. proj, u= (Di+ Oi+ (Dk…

A: Given : u = i+6j+2k v = 2i-2j+5k

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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

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Q: The volume of parallelepiped determined by the vectors u = 2i – k, v = 2j – 3k and .= w = i + j+k is…

A: We use the definition of the volume of a parallelopiped determined by the vectors a, b and c to find…

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

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Q: Find two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: Given that a→=j+2k,  b→=i-2j+3k   We know that the cross product of two vector is perpendicular to…

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

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Q: What is the angle between the vector i + v3j and the positive direction of the x-axis?

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Q: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

A: To find the normal unit vector perpendicular to A and B

Q: Prove the stated property of distance between vectors.d(u, w) &lt; d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

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: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

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Q: (a) Calculate the dot product and angle between two vectors, where u 7j– 2k and v = (1,2,3).

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

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Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

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 dot product of the vectors v = 5i - 3j and w = 2i - j.

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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: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

A: u=-3i+2j-5k,  v=i-j+4k Now the vector orthogonal to both u and v is, w=u×v=…

Q: Find the angle between the vectors u and v to a nearest degree: u = j + k, v = i + 2j – 3k

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Q: Calculate the triple product u · (v × w) of the vectors u = 3i − 2j − 5k, v = i + 4j − 4k, w = 3j +…

A: Calculate the triple product u · (v × w) of the vectors u = 3i − 2j − 5k, v = i + 4j − 4k, w = 3j +…

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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