Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is 45°.

Q: Find the vector v with the given length and the same direction as u.||v|| = 4, u = (−1, 1)

A: To find a vector v with the given magnitude of ||v|| = 4 and in the same direction as u = (−1, 1).

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: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

Q: Find the angle 0 between the vectors. u- (3, 2, 0), v = (-2, 3, 4) radians

A: u=3, 2, 0  &  v=-2, 3, 4 Now, u·v=3-2+23+04=0 Now the magnitudes is,…

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

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Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

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: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k b. u = 2i – 2j + k, v= 3i + 4k а.…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 4t, y = 4 –…

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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: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

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Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

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Q: The angle u= between the two vectors \(\) and U= is equal to 0=T

A: We know that angle between two vectors is given by θ=cos-1u→·v→uv Here, u→=-4,2,1 and v→=-20, 10, 5.

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: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Find the angle between the vectors v and w v = (2, 1, 3)T , w = (6, 3, 9)T

A: We need to find the angle between the two vectors.

Q: Find the angle between the vectors v and w v = (2,−3)T , w = (3, 2)T

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 8 –…

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Q: Determine a unit vector in the direction in whichf(x,y) = 4x³ y² increases most rapidly at point…

A: Given that : - f(x,y)=4x3y2    at  P(-1,1) A function f(x,y) increases most rapidly at pointy P(a,b)…

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: Find the angle 0 between the vectors. f(x) = 3x, g(x) = 4x?, (f, g) = | Rx)9 f(x)g(x) dx radians

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Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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

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

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Q: Ã = ë, + 3ểy – 2ể, : Calculate the angle between the B = 4ëx – ëy : vectors A* and B". = -3e, - 5ẽ,

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Q: Find the angle e between the vectors. -(cos , sin 2), v- (cos , sin. x radians

A: Given that, u=cos3π4,sin3π4 and v=cosπ6,sinπ6. It is known that, the formula for u·v=u·v·cosθ.…

Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

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: Find the angle 0 between the vectors. 3x, g(x) = x, (f, g) = (x)g(x) dx %3D !! radians

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Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

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Q: Find the angle 0 between the vectors. (c0 ST, sin S), v- (cos , sin ) 5Tt 4 COS 3 COS 4 radians

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

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Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k

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

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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: Find the angle between the vectors i + j + 2k and 2i - j +k

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Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k а. -

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

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Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Find the angle a between the vectors 日- 2 and a =

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Q: Find the angle e between the vectors. u = (0, 0, 1, 0), v = (3, 3, 3, 3) radians

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Q: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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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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