Q2/ If A=ai+bj+3k, B= 2i+3j+4k, C-i+j+6k are vectors , perpendicular to B and A is perpendicular to C, find the constants a and b.

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

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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 v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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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: 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: according to what you learned from the vector addition experiment, if we have vectors à = 2.4x – 3ŷ…

A: Given that,a→=2.4x⏞-3y⏞b→=4x⏞+5.5y⏞x⏞ and y⏞ are unit vectors representing positive x and y…

Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

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Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

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: Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

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Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

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Q: Choose a vector (b1, b2, b3) for which Ax = b can be solved, and another vector b that allows no…

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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: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

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

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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: 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: What is the area of the parallelogram determined by the vectors v = (1, 3, 6) and w = (-1,0, 3)?

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Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

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Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

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

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Q: Determine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work…

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Q: 9. Explain why four vectors is R³ are always linearly dependent.

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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 area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R3 if x = [1,-2,4] and…

A: Cauchy schwarz inequality -  For any vectors u and v in an inner product space V,  |<u,v>|…

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: Find two vectors v1 and v2 whose sum is , where v1 is parallel to while v2 is perpendicular to . v1…

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Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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

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

Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: What is the value of each of the constants that are part of the linear combination between the…

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

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

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Q: Hi, any help on this problem would be greatly appreciated. Thank you!

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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: A n = i-j+3k, n2 = 2i +j+ 3k to the two vectors.

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Q: Find the area of the parallelogram defined by the vectors ä= (2, -2,0) and 6= (0,1,2)

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

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Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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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 two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

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Q: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

A: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

Q: Verify that the vectors a = (2, 5, –1) and b = (3, –1, 1) perpendicular. а. are

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Q: a) tor which values on a are the vectors 87 2 -- a linearln independent?

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Q: Find two vectors and īz whose sum is (-4, -2), where vy is parallel to (-2, -5) while ū, is…

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Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry