a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides of a right triangle.

Q: Given two non-zero vectors a and b such that abs(a+b)=abs(a-b), find the value of a*b (dot product…

A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

Q: Consider A = ⟨0, 4, 2⟩, B = ⟨6, −1, 0⟩ and C = ⟨3, 0, 1⟩. draw the vectors A, B, and C in…

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Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

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Q: The figure below shows four named points A, B, C, and D on a grid generated by two vectors ₁, ₂ in…

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Q: a.A = 6-j8, B=8-j6 bA=6+j8, B=8-j6 c. A = 6-j8, B=-8+j6 C.

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Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

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Q: Evaluate: if vector OA = (2,3) and OB (-1,-2) Show all steps please

A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

Q: how that vectors[ A-2i+ 3j - 2k,B=I +2j+ 4k ] are perpendicular to each o

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Q: Draw à = 3î + 2ĵ+ 5k. Must Include the Rectangular Prism used to draw 3D vectors.

A: a⇀ = 3i^ + 2 j^ + 5k^ The given vector indicates a 3D vector :  3 units in the direction of x-axis…

Q: 5. Add vectors 2i– 2j & i+5j by a) Graphing these two vectors in a coordinate system in standard…

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Q: Determine the real number ? such that vectors a = 3i + 2j and b = 6i + ?j are orthogonal.

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Q: Find the area of the triangle with vertices (1, 1, 2), (2, 3, 5), and (1, 5, 5). Use vectors and…

A: Consider the given question, Let the vertices of the triangle ABC is A(1, 1, 2), B(2, 3, 5) and C(1,…

Q: ulate the angle between the two vectors i +2j+ 3k and 3i - 2j+ k er your answer in the box below,…

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Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: Let -4 -1 7 -11 3 -1 A 13 -1 1 -3 13 -1 1 -3 Find orthonormal bases of the kernel and image of A.…

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Q: Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

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Q: Find the cross products u xv and vxu for the the vectors u = 2i-j-2k and v= i +3j - 3k. U XV= i+ j+k…

A: (.) Given vectors are,      (.) Corss product of two vectors  and   is given by,           &…

Q: Find the acute angle formed by two diagonals of a cube. (vectors) show complete solution.

A: It has been assumed that the length of each side of the cube is a unit.

Q: The projection of the vector 11i + Aj in the direction of the vector i+3j is the vector 2i+6j. What…

A: To find the value of A for which  Projection of vector (11i + Aj) in the direction of the vector (i…

Q: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

A: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

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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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.