If the points with position vectors 10i+3j.12i-5j and ai+11j are collinear, Find the value of a.

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

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Q: Show that each pair of vectors is perpendicular.     -4i -3j and 6 i - 8j

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Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: Given the two vectors A = -9i- 2j -7k and B = -3i- 4j +8k, Find th (e) Ax B (f) the angle between…

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Q: Find the area of the parallelogram that has the vectors as adjacent sides. AB= 6i + 6j - 6k, AD = 6i…

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

Q: .If the position vectors of the points A, B, C, D are a = i+j+k, b 2i + 3j, c= 3i+ 5j - 2k, d k-j.…

A: Given:  a=i+j+k, b=2i+3j, c=3i+5j-2k, d=k-j We know that if A=x1i+x2j+x3k, B=y1i+y2j+y3k then…

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: If the position vectors of P and Q are i + 3j- 7k and 5i- 2j+ 4k respectively, find PQ and determine…

A: The equation of the line, PQ passing through the points P and Q is defined as follows.…

Q: PQRS is a parallelogram and X is on the side QR. If vector PQ=3i+j, and  vector XQ=2i+j. find PX.

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Q: for what value of Ca) will the Vector ū = -41-8)4ak,ū =ei+4j-5k are parallel

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Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

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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: Given the vectors u=-i+3j, v=6i-6j, w=-5i+3j, carry out the designated equation. V*(u+v)

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Q: Given the vectors u = -i-4j and w=-2i+5j, find 7u and u – w. | Write your answers in the form ai+bj.…

A: Given the vector u = -i - 4j And w = -2i + 5j Find 7u and u - w in the form of ai + bj.

Q: What is the angle of vectors A=5m West and B=15m 60° North of West?

A: The vector A can be written as: a=-5i The vector B is 60 degree north of west that means it makes an…

Q: Show that the points with position vectors 3i−5j, 4i+j, 6i+13j are collinear. If the point whose…

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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: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

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Q: The vectors A 6i + 4j – 8k and B = xi + 6j + zk are known to be parallel. Find x and z x = 9. -12

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Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

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Q: Use the given vectors v = -8i - 3j, w = -10i - 5j to find v.w and v.v

A: Given          v=-8i-3j ,          w= -10i -5j

Q: Given the points A: (1,6,3) and B: (2,-3,3), find the vector ü = AB %3D

A: To find- vector u.

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i, v = -3j

A: Given vectors: u=2i+0j+0k and v=0i-3j+0k u×v=ijk2000-30u×v=i0×0-0×-3-j2×0-0×0+k2×-3-0×0u×v=-6k The…

Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: Given the vectors, a = (4,-5) and b = -10i -8j: %3D a. Find a - 2b.

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Q: Given initial point  P1 = (−7, 4)  and terminal point  P2 = (9, 6),  write the vector v in terms…

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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: Given the vectors u = -i-4j and w = -2i+5j, find 5u and u +w. Write your answers in the form a i+bj.

A: Given:- u=-i-4j  w=-2i+5j   then, 5u = 5*(-i - 4j) = -5i - 20j Here , a= -5 and b=-20

Q: Given the vectors v = 2i+ 3j – k and w = 4i – 2j + 3k. Find the angle between v and w. %3D

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Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: Given initial point  P1 = (2, 5) and terminal point P2 = (−1, 6),write the vector v in terms of i…

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Q: Find the angle in degree between the two vectors as indicated in the rectangular box of dimension…

A: The dimension of the given box is 1×2×3.

Q: Use the given vectors v = -6i - 5j, w = -10i - 8j to find v.w and v.v

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Q: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

Q: If c = 14, is the vector 2i + 5j in the span of ci – 12j and 7i - 6j? If c # 14, is the vector 2i +…

A: Answer

Q: Use the given vectors v = -8i - 3j, w = -10i - 5j to find v . w and v . v.

A: Consider the given vectors v and w. First calculate the dot product for v and w.…

Q: Find the equation of the perpendicular bisector of the line join- ing the points with position…

A: From the given information we can draw this figure

Q: ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD. Vectors

A: Consider the given information. Let's draw the triangle.

Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. Enter the vector i as i,…

A: here here we have

Q: ABCD is a parallelogram, where A, B and C have position vectors i + 2j – k, 2i + j- 2k and 4i – k…

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Q: Given the vectors v = 4i + 2j + k and w = 3i – 4j + k. Find the angle between v and w .

A: We know, the angle between two vectors v→ and w→ is θ = cos-1v→·w→|v→| |w→|

Q: Given the vectors i = - 2i - 6j and v = 8i – 5j, perform the operations below. u + =

A: Vector problem....

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

A: The given figure is:

Q: Show that each pair of vectors is perpendicular.     -6i -5j and 10 i -  12 j

A: If two vectors A and B are perpendicular then its dot product A.B=0Dot product:i, j,k are the…

Q: Given two vectors P = 9i + 9j + (-9k), Q = (-6j) The angle between the two vectors is

A: We have two vectors P=9i+9j-9k and Q=-6j. Then the angle between the two vectors.

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.