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

Q: Find the length of the vectors (a) 2i⃗ +3j⃗ −k⃗

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: The vectors A 5i + 7j – 8k and B 3i + yj + zk are known to be parallel. Find y and 2 y = = Z

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Q: Find the cosine of the angle between the vectors: a = 4i + 2j-k b=2i+ 4j-k

A: Simply take the dot/scalar product of both vectors a & b.

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: What is the cross product of the vectorS 2i + 3j + k and 61 + 9j + 3k? Explain why your answer is…

A: Cross Product: Cross product of two vectors is the method of multiplication of two vectors. A cross…

Q: Given the vectors, ū = -3i+2j and = 4i – j, find 4ü-27. %3D (-20,10) (20,-10) (-20,-10) (20,10)

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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: Let u =j- 3k, v = - 9i + 3j – 3k, w = 3i -j+ k. Which vectors, if any are (a) perpendicular? (b)…

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Q: b) Consider the vectors a = 3i - 2j+7 K, and b = -5i +4j-3k, find 1-a.b 2- Angle between a and b. 3-…

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Q: if these vectors A = 4i – 2j + 4k and B = 4i + 5 j

A: we have ;  A→=4i-2j+4k ............(1)B→=4i+5j+0k  ...............(2)

Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

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 vectors u = /2i - 9j and v =v2i+j-2k.

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Q: Find the value of b so that vectors U = 5i +12j and V = 4i + bj are perpendicular.

A: Given :          U=5i+12jV=4i+bj

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: For what value or values of a will the vectors u = 2i + 4j - 5k and v = -4i - 8j + ak be parallel?

A: Given,

Q: Find the cross product of the vectors a = 2i + 3j – k, b =i- 2j + 2k.

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

Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

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

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Q: 2. Consider the two vectors a and b, as graphed below. 2a Plot the result of a +b on the same axes.…

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Q: Find the angle between the vectors a 0 = and b = 2i+j - 4k. 10i - j - 5k

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Q: Given the vectors u = -i-5j and v =-3i+2j, find u v

A: Given vectors are  u=-i-5j     and   v=-3i+2j

Q: Determine if the vectors v = 3i i, and w = 2i -6j are parallel or not. Explain.

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Q: ind the value of a so that vectors U = ai + 9j and V = 3i + 3j are

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Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: Show that each pair of vectors is perpendicular.     2i + j and i - 2j

A: Solution: Consider the given vectors are  a→ = 2i + jandb→ = i - 2j We know that if the dot product…

Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular…

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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: Find the angle between the vectors u = (2, 5) amd v =

A: Given: There are two vectors: u=2,5v=4,-3 To determine: The angle between the given two vectors.…

Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: (b) Check whether u = 6i – 2j+k and v = = -4i – 3j+9k are parallel or not. Then, find the area of…

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Q: The value of A for which the vectors 2i- 4j + Ak and 3i- 6j + k parallel are

A: Given the two vectors Let's say v1 and v2 v1= 2i-4j+lemdak v2= 3i-6j+k

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: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

A:

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

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Q: Find the angle a between the vectors 3 2 B [B] and -4 -3

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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: Express the vectors in terms of their lengths anddirections. i + 2j - k

A: Given:  i + 2j - k

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

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Q: 3- Rewrite the vector v in the form a + ib, where vectors a and b have only real components.

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Q: Find the angle between the vectors i – k and 4i + 4j -2k

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Q: Find the angle 0 between the vectors a = 8i – j– 4k and b = 2i+j- 9k. %3D

A: A vector is a mathematical concept with both magnitude and direction. It's used to describe things…

Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.