Consider two vectors →A=Ax^i+Ay^j+Az^k and →B=Bx^i+By^j+Bz^k. Scalar product of these two vectors can be found out by following two different formulae. →A⋅→B=AxBx+AyBy+AzBz. →A⋅→B=ABcosϕ Prove that the above two formulae for scalar product of vectors are equivalent.

Q: 4. Express PQ-RQ+SR-PS+RS as a single vector.

A: Expression

Q: Are these vectors linearly dependent or independent? p1(x) = 1, p2(x) = 1 + x, p3(x) = 1 + x + x^2,…

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Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: How do you know if 3 vectors span R^3? Is there any example?

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Q: We know that there are two ways to multiply vectors: the vector and scalar product. How about vector…

A: Vector division is not possible .

Q: Find a vector orthogonal to both and . Please provide a detailed explanation of the process to get…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are write both vectors in…

Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Write the vectors (1, 0, 0) and (0, 0, 1) as linear combinations of vectors {(1, 0, -1), (0, 1, 0),…

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Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: v1 = (- 3.7) and v2 = (5.5) vectors Does it form a base for R^2? Why is that?

A: Given V1=(-3,7) and V2=(5,5) To check V1 and V2 are basis for R2.

Q: When multiplying a scalar and a vector: |ha|=|ā| when A |xa|=|||ā| when > + 0 and + 0.

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Q: Please justify whether these statements are true of false. a. If u and v are vectors in R^3, then…

A: Objects with both magnitude and direction are called vectors. The vector's size is determined by the…

Q: Find a unit vector in the direction of

A: Given that,   vector = <6, 3, 2> = u¯ (Say)   Unit vector = u¯u = <6,3,2>62+32+22 =…

Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

A:

Q: 4) IF = (6,-8) m, B = (-8,3) m, AND A = (26, 19) m, FIND THE UNKNOWN CONSTANTS AND B SUCH THAT ab +…

A: As Per Bartleby Answering Guidelines We Solve  Only First One Problem Solution - 4  :  Given that…

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: Find a unit vector in the direction of

A: Let us consider the given vector as,

Q: In R^3, consider the three points A(2, -1, 4), B(3, 4, -2) and C(-1, 2, 7). (a) By an appropriate…

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Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

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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