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

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Use paper and pencil to identify the redundant vectors. 4 3. 0. 0.

A: Definition : Redundant vector in a set is a vector which can be written as linear combination of…

Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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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: a/Find the length and diredtion of the vector 式ド、で Aュ2i+3k where や ノ

A: The given question is from vector and can be solved as shown in step2

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: The dot product of two vectors X1 y1 y2 and y = X2 Xn Yn ... 18

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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: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

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

A: Let's find.

Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

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: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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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: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

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Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

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: 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: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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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: solve for th e vector x in terms of the vectors a and b. x + 2a - b = 3(x +a) - 2(2a - b)

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

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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: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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Q: Find the angle O between the vectorS 3. and -2

A: Given: 34-2 &114 We can write given vectors as, u=3, 4, -2v=1, 1, 4 We know that,…

Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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Q: Find a unit vector in the same direction as (2i - 6j - k). Oi-j-k O

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Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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

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Q: Determine whether the vector U = 2 is a linear combination of the vectors Xi = 2 X2 = and X ? Give…

A: Let  U→=aX1→+bX2→+cX3→  Where, a,b and c are scalar. Then,…

Q: Find the angle 0 between the vectors i + 2j - 3k and -i + 2j + k.

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Q: Find the angle between the vectors i + j + 2k and 2i - j +k

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Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

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Q: Q1// Determine äxb if å=3i-5 j+7k and b=2i-6j+4k and check if resultant vector are perpendicular to…

A: Given,           a→=3i-5j+7k and b→=2i-6j+4kTo find: a→ × b→

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: Find the dot product of the vectors v = 5i - 3j and w = 2i - j.

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Q: Find the addition of the vector using the component methods. 1. 9 m/s [N30°E] and 2 m/s [N 60°E].

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Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

A: