7. For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||*||b|² – (a - b)²

Q: 2) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.3., # 46 or from your…

A: Solution

Q: Prove the Py the goreen th : ortho gonel vectors product spoce V. Prove Suppose O and v in an inner…

A: we know that ||u+v||2=<u+v,u+v> now,…

Q: Among all unit vectors u = in R°, find the one for which the sum x + 6y + 9z is minimal. నా

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Q: Prove that for any non-zero vectors a, b, a · b = |a||b| cos(0), where 0 is an angel between a and…

A: Consider the n -dimensional vectors a and b , where n≥2 . The vectors a , b and a−b can be…

Q: 3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

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Q: Please help me number 6. Thanks!

A: We are given that the unit vectors x, y, z satisfies the equationTo find the relation between the…

Q: Among all unit vectors u = in R°, find the one for which the sum x + 3y + 8z is minimal.

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Q: 1. FroiI Show that cos a + cos B + cos y = 1 2. Use the figure from Ex. 1, to show that two nonzero…

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Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

A: Here, given that a=-5,2,1,b=-3,-4,3. To find scalars s and t such that: s a+ t b=-7,-18,11 That is:…

Q: 16 Jlg wo vectors ñ and m are said to be orthogonal if ħxñ=0 ulgo O ihs o

A: Two non-zero vectors are said to be orthogonal when (if and only if) their dot product is zero.

Q: Let a = (-4, 5, -1) and b = (0, –3, 2). Show that there are scalars | | s and t so that sa + tb =…

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Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

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Q: The dot product of two vectors Xị yi X2 and y y2 Xn Yn in R" is defined by x · ỷ = x1yi + x2y2 + ...…

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Q: (e) 5. Compute the angle between the vectors [1, –1,0, 1] and [0, 1,0, 2]. 6. Compute the…

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Q: is Cartesion Tensor o& orden 2 on the for m 3 a=(3,4,1) Find - 2 %3D Tią and a. I

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: A vector A-xyzi+3x'yj+ (xz-y'z) k.

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Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

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Q: 2. Let u e R" and v E R" be two non-zero vectors, in other words at least one component of the…

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Q: 3. The work Wdone by = xf + 3xyj - (x + z)k to move a particle from point 1 to point 2 is defined by…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

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Q: 1 Find the length of the vector x = -4 -5 Enter 'sqrt(a)' for va. ||F| =

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Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: 3) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.5., # 7 or from your…

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Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

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Q: Prove that the vectors u = (cos θ, −sin θ) and v = (sin θ, cos θ) are orthogonal unit vectors for…

A: Given Data The first vector is u=(cos θ, -sin θ). The second vector is v=(sin θ, cos θ).   The…

Q: (1) Let x and y be the vectors x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z is…

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Q: 1) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.1., # 37 or from your…

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Q: The vector w is a unit vector, and the vector i is any non-zero vector. If z = (x · W)w and ỹ = i –…

A: Use the property of dot product and associative and distribute property to solve the problem.

Q: (1) Let x and y be the vectors -- -- -) x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z…

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Q: For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||2||b||? – (a · b)? ах

A: Use the vector product and scaler product identity, a×b=absinθn^…

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: 24- If the vector A = 2i + 4j – 3k in the primed triad i/ j/ k/ in which the x/, y/ axes are rotated…

A: Vectors are the quantities which represent magnitude as well as direction. The unit vector i, j and…

Q: 3. For any vectors U, V and scalars a, b, prove that (a) (aU) x (bV) = ab(U x V)

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Q: Let FE R?. Show that F = õ if and only if F. Ã=0 for all vectors Ā E R?. [This is a proof, be sure…

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Q: Let a = (4, 5) and b = (2, –2). Show that there are scalars s and t so that sa + tb = (2, – 20) You…

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Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

A: Let u and v be tthe vectors in 3-spaceThen by Lagrange's identity,we haveu×v2 =u2.v2-(u.v)2…

Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

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Q: When is the vector x = (3) orthogonal to the vector y = ()? You may want to go through the proof of…

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Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

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Q: Suppose R3 has the Euclidean inner product. Apply the Cauchy Schwarz inequality to the vectors = (a,…

A: We have to proof the inequality using cauchy schwartz  inequality

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: 3) Prove for any two vectors à = (a,,a2) and b = (b,, b2) in R2 the angle between them is %3D d-b 0…

A: We use this formula to proof our result.

Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

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Q: Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch the…

A: a=-2, -1, 0b=-4, 1, 3sa+tb=s-2, -1, 0+t-4, 1, 3=2, 4, 3-2s-4t=-2s+2t=1 ...(1)-s+t=4 ...(2)3t=3…