10. Given à = (3,-1,5) and b = (2,1,-8), find: a) 3ā + 25 Ans: b) āxb Ans: c) the unit vector in the direction of a Ans:

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Let a = (2, – 3) and b (0, – 3). - - Find the angle between the vector, in degrees.

A: Given a→=<2,-3>           b→=<0,-3>

Q: For the three vectors a, band, it is found that ax statement below is true?

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Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Find the angle between the two vectors and determine if they (section 9.5/9.6) are orthogonal: BAGU…

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Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: .b,č are three vectors such that a + b+ e = 0, lal = 5.6 = 3. = 8 then ä.b+ ans. -49 48 1/6

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Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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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: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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Q: The vector which has length 2 and direction opposite to u?

A: We have the given vector as u=-122   We have to find a vector that has length 2 and direction…

Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

A:

Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: 1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is…

A:

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Find Hhe voluie af Mee Parallelepiped daterimıned by he vectors a,b and c. (a) (,2,3)and…

A:

Q: Suppose we know that u · v = u · w. Does it follow that v = w? If it does, give a proof that is…

A:

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

A:

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

A:

Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

A:

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

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

A:

Q: a. From the set of vectors{ (1, 2, –1). (-4, –5, –6), (4, 3, 10). (5, –3,2)}. select two pairs of…

A:

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

A:

Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

Q: The vector from the origin to point A is given as 6ax – 2a, – 4az, and the unit vector directed from…

A: Given vector is A→=6,−2,−4 and B→=B23,−23,13 And B−A=10 We have to find the coordinates of the point…

Q: Given the vector u , can you find 1. A vector in the same direction as u but with length 1? Enter…

A: Given a vector 'u'. We need to find vectors in the same direction of 'u' but with length 1 and 6.…

Q: The length of the vector c = (2, -3, 1) is %3D

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Q: Consider the vectors ā (2, 3, –1) and b = (4, –9, 6). Find the cross product of a and b

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Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

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Q: The vectors (8, 6) and (k, 12) are parallel. What is the value of k

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Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

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Q: Since A, B and C vectors are perpendicular to each other, A, B, C, =? A -6) â, 1 (8) â, + A‚⸠B 19)…

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Q: Describe a unit vector in R^3 with the same direction as <1,0,7>

A: Consider the given point vector

Q: Find a vector a that has the same direction as (-10,7, 10) bưut has length 4.

A: In the given problem we have to find a vector a that has the same direction as -10, 7, 10 but has…

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A:

Q: What is the angle in degrees between the two vectors (2, 4. -1) and (4, 8, -2)? Note that the…

A:

Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

A:

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

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Q: 4. Find a unit vector that is perpendicular (5, 6). to

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.