Find v|, for the following vectors: (6) v - [ (6) v = [-] (6) v = [ 3 V (d) v =

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: Find two vectors v, and 02 whose sum is (-5, 5, –3), where 0 is parallel to (-1, –2, 1) while Dz is…

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Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

Q: Find the dot product of the pair of vectors (-2, 5) and (4, 1).

A: Given : < -2 , 5 > and < 4 , 1 >

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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Q: Find two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Find two vectors v1 and v2 whose sum is (2, –5), where vj is parallel to (5, 2) while v2 is…

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Q: Find two vectorsī and 02 whose sum is (2, –4), where v, is parallel to (2, -4) while vz is…

A: We have to find vector v1 →and v2→   the sum of vector v1 →and v2→ is 2, -4   vector v1 →is parallel…

Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: If it is known that the internal product of the vectors ā (4, x, -2) and ƃ (1, x + 1,5) is 6,…

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Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Two linearly independent vectors in R3 span R2, is that true

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Q: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: photo is attached

A: Given informationVector V = (-3, 5)

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7) r(t)…

A: Given: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7)…

Q: how can i learnd about vector in r2 and r3?

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Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

Q: Find the smallest positive angle between the given pair of vectors. (3,1) , (4,6)

A: The given pair of vectors are,

Q: Q2: Determined the component of the vectors at each point…

A:

Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Realize the Cauchy-Schwarz inequality for the vectors x= ( -1, 2, 4,3), y=(0,-2,1, 4) ∈ R4 and find…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

A:

Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

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

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: What helps to set of vectors linearly independent?

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Q: Write the vector v= 1 as the linear combination of vectors --0 w =

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Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: When is a vector incomprehensible and when is a vector irrational?

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Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

Q: Find a non-zero vector perpendicular to the vectors -2 and ü = 2 ||

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Q: Find self-value and self-vectors.

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Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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Q: Find two vectors vj and 2 whose sum is (-2, -5), where is parallel to (-3, 4) while vz is…

A: Solution: The objective is to find the vectors