For vectors v and w E R, show that: (a) |u x v||? = ||u||2 ||v||2 – (u - v)2 (b) ||u x v|| = l|u||v|| sin 6, where 0 is the angle between u and v.

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Suppose f(x, y) = / tan(x) + y and u is the unit vector in the direction of (0, –1). Then, (a) V…

A: Given fx,y=tanx +y To do 1∇fx,y2∇f-0.7,63fu-0.7,6 =Duf-0.7,6

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A: Given information: The values of the partial derivatives of the function are fx(0,1)=3, fy(0,1)=2.…

Q: Find cos(0) if 0 is the angle between the vectors u= 2i + 2j – k and v = 3i + 4k

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Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

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Q: Given the vector function: *(t) = (1+ sin (3t), tan (2t), t) Relate the vector functions to the…

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Q: When the angle between vectors u and v is between 0° and 90°: || You can't tell O t • 0

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Q: Let 0 be the angle between vectors A and B, find the value of the angle 0 when -6V3A × B = 18Ã. Ē

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Q: If θ is the angle between two nonzero vectors u and v, then cos θ = ________.

A: If θ is the angle between two nonzero vectors u and v, then    cos (θ) = (u.v)/(||u|| ||v||)

Q: Prove that u = (cos θ)i − (sin θ)j and v = (sin θ)i + (cos θ)j                               are…

A: We have given;  u = (cos θ)i − (sin θ)j and v = (sin θ)i + (cos θ)j

Q: (a) Find the unit vector of 2q where q=(8 sin 0,-8 cos 0,0).

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Q: Find the angle 0 between the vectors. u = ( cos sin 4 V = ( cos sin 3 4 radians

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Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when

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A: Given: F=-3j

Q: at Q6:- If w = xi + yj + zk nonzero vector. Then show that cos a + cos? B + cos? y = 1, where a, B…

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Q: Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make…

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Q: Consider the vectors u = ⟨cos , sin , 0⟩ and v = ⟨cos , sin , 0⟩, where > . Find the dot product…

A: Consider the given vector u→=cosA,sinA,0 and v→=cosB,sinB,0

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Q: Given the unit tangent 1 (-2 sin t, 1, 2 cos t), V5 U = and unit normal vector: n = (– cos t,0, –…

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Q: Find the angle between the vectors u = cos( /6)i + sin( /6)j, v = cos( 3/4 )i + sin(3/4 )j     (a)…

A: u=cosπ6i+sinπ6j,  v=cos3π4i+sin3π4j Now,…

Q: The vector êr and êe in terms of î and ĵ is given by êr = î cos e + ĵ sin 0, %3D and êe = -î sin 0 +…

A: True

Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

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Q: Find the angle in degrees between u = (1, 2, 0) and v = (1, -2, 1)

A: Given, u=1,2,0v=1,-2,1 The formula for finding the angle between the two vector is, cosθ=u→·v→u→v→

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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: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when |-5V3A x B = 5Ã.B

A: To find the angle θ between vectors A and B. It is given that,

Q: Find the angle 0 (in radians) between the vectors. sin + sin u = cos 4 v = cos 4 + sin 4

A: Trigonometry used:

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Q: If F= (xà) - ( x6), show that where r is the position vector and a,6 are constant vectovs

A: Here r is position vector and a and b are constant vectors

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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: By vector methods find the angle between the line x = y = 2z and the plane x + y + z = 0.

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Q: Find the length and direction (when defined) of u x v and v xu. u= 2i - 2j - k, v=i-k

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Q: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

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Q: Suppose that |u| = 6 and |v| = 9, and that u times v = -37. Find the angle θ between the vectors u…

A: Vector Question