(1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle ABC, let a, b and c denote the length of BC, AC and AB. Based on the above theory, try to prove that the area of the triangle ABC equals to VP(p – a)(p – b)(p – c) where p= (a+b+c)/2 B

Q: find the angles between the vectors:x+y=1,2x+y-2z=2

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: Find the angle (in radians) between the 2 vectors U(-3, 4, -4) and V(1, 2, 2)

A: Given vectors are,               U(-3, 4,-4 ) and V(1, 2, 2 )

Q: 5. Determine the value of a so that the vectors v = perpendicular. (a,3, -2) and v - (2, -2a, 1) are

A: Solve the following

Q: A. IF V = yi - x), find curt(V) and V.V B. Find the value of the constant B such that the vectors: u…

A: We can find the curl and divergence of vectors by using the formula The condition for the vectors to…

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: a) Let a = 2i – 3j + xk and b = -3i + j + xk. Find the values of x for which vectors a and b are at…

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Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: 8. Determine the angle between the two vectors. a) Ã = and B = b) Ả = -2î + 3 + 5k and B = î + 2j…

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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: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: For what values of c are the vectors [-8, c, 4] and [c, c²,c] orthogonal?

A: For orthogonal,dot product of vectors is equal to zero.

Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: Find the angle between the pair of vectors below. u = (2,3) and v = (-2,5)

A: Given query is to find the angle bothe vectors.

Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

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

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Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: a) Given: v1=<-3,6>,…

Q: Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is…

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Q: If au + bû = 0, where a and b are positive. If a = -b, what must be true of vectors ū and v? Explain…

A: The relation between a and b is a=-b. Also, the relation between vectors u⇀ and v⇀ is au⇀+bv⇀=0⇀.

Q: Determine the angle, to the nearest degree, between the vectors= (4,6,-2) and y = (1,8,2)

A: Solution is done in step 2

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: (a) the dot product of the two vectors a(-2,5) and b(3,6) a · b = ax · bx + ay · by = -2 · 3 + 5 ·…

Q: Find the measure of the angle between the two vectors. 1) u = (4, 9) v=(-3, -8) 2) u = (-8, 9) v =…

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Q: 2. If å and b are two vectors with lengths 2 and 5 and angles between 150°, respectively, obtain the…

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Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

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Q: A=4+J1 and B=2+j3 respectively determine the sum and the difference of the vectors in both…

A: Concept: Complex numbers: Complex numbers are two-dimensional complex or s-plane points that are…

Q: A triangle in R3 has two sides represented by the vectors = (2, 3, –1) and OR = (1, 4, 1). Determine…

A: Topic:- vector algebra

Q: Find the angle θ between the vectors.p(x) = 1 + x2, q(x) = x − x2, ⟨ p, q⟩ = a0b0 + 2a1b1 + a2b2

A: +

Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

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

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Q: 1. Find the angle between two vectors u = i-2j - 2k and v= 6i + 3j+2k.

A: Given two vectors u→=i-2j-2k and v→=6i+3j+2k. Here find the angle between two vectors.

Q: A = x6- y9+z3 B = x6- y3+z9 C = x 2- yl-zl For the given vectors A,B, and C show that whether C is…

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

A: result of vector cross product of two vector is perpendicular to both the vectors.

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: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: 2. The area of the triangle whose adjacent sides are the vectors u and v is a) Ju · v| c) |u x v|…

A: It is known that, the area of the triangle whose adjacent sides are the vectors A and B is 12A×B.

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

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 (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: a) If u and v are two-dimensional vectors, we calculate the dot product as   u=(u, u2) and v=(v1,…

Q: b. Find the angle between the vectors u = (18, –1, –7) and v = (-37,35, 2)

A: u = (18, -1, -7),  ∥ u ∥ = √[(18)2+(-1)2+(-7)2] = √374 v = (-37, 35, 2), ∥ v ∥ =…

Q: a-(:) We have two vectors: a = and b= What is the resultant of -a plus b? (

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Q: Find the angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^