Let ā = 2 and b a) Find the area of the parallelogram formed by the two vectors.

Q: If the volume of the parallelepiped determined by the vectors A = i +ak, B = 8i-5j + ak and C = 2i…

A: Given vectors are A = i + αkB = 8i - 5j + αkC = 2i + 3j - 8k

Q: Prove the stated property of distance between vectors.d(u, v) = d(v, u) for all vectors u and v

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: Find the volume of the parallelogram in which the vectors (S, T, R) are adjacent sides whose values…

A: Given: The volume of the parallelogram of the vectors (S, T, R) that are adjacent sides can be…

Q: The sides of an isosceles trapezoid have lengths 3cm, 15cm, 21cm, and15 cm. Draw a diagram and show…

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Q: Find the area of the parallelogram spanned by vectors v and w suchthat ||v||=||w|| = 2 and v · w =…

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Q: If the volume of the parallelepiped determined by the vectors ä, 5, č e R³ is A cubic units, which…

A: Consider the provided question, a→∧3b→∧b→∧c→Let a→∧3b→=u→a→∧3b→∧b→∧c→=u→∧b→∧c→…

Q: Use the cross product u ✕ v to find the obtuse angle between vectors u and v, where u = −i + 6j +…

A: The answer is in step 2.

Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The area of the parallelogram determined by the vectors u and v is A=u×v. Given u = i + j and v = j.…

Q: B. Explain with sketch how can calculate the volume of parallelepiped by three vectors?

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Q: If the volume of the parallelepiped determined by the vectors A = i + ak, B = 8i - 5j + ak and C =…

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Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the volume of the parallelepiped determined by the vectors ?, ?, and ?.   a= i + j,   b= j +…

A: a=  i + j+ 0k b= 0i + j + k c= i + j + k  The required volume is [a b c]=110011111 =1111-0111…

Q: Find the volume of the parallelepiped determined by the vectors a =i+3j-k, b= 4i+j-2k and c= - =…

A: a=i+3j-k,  b=4i+j-2k  &  c=-2j+5k

Q: Suppose that u and v are unit vectors in R°. If the angle between u and v is T/4, then what is the…

A: Given that vectors u and v are unit vectors and angle between vectors u and v is π4.  We know that…

Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The vectors u, v, and w. u=i+j-k,v=2i+j+k,w=-i-2j+3k.

Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Q6. Find the volume of parallelopiped formed by the vectors , and .

A: To find the volume of the parallelepiped formed by given vectors.

Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

A: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

Q: Find the area of the parallelogram determined by the given vectors. 3 u = 2i – j+ 3k, v = ÷i + 2j –…

A: If vector a and vector b are the two adjacent sides of a parallelogram then the area of the…

Q: Find the area of the parallelogram with vectors a = 3p+ 2q, b= 2p-qwhere \pl = 4, lq] = 3, (p, q)…

A: To find the area of the parallelogram with the vectors a=3p+2q,b=2p-q where p=4,q=3,p,q=3π4.

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

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Q: If the two vectors are in the following figure, find an area parallelogram A=i+j-k B=2i-2j+2k

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Q: Use the cross product u x v to find the obtuse angle between vectors u and v, where u = i +8j + k…

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Q: Prove that the diagonals on the parallelogram in the figure intersect at their midpoints. (b, c)…

A: let A=(b, c) B=( a+b , c) D=(0,0) C=(a,0)

Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az * O…

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Q: Given the vectors a=i + j + k,  b= i-j and c=i + 2j + k, determine the volume of tetrahedron

A: Given- Given the vectors a = i + j + k, b = i - j, and c = i + 2j + k.  To find- Determine the…

Q: Q) write down the application of cross dot scaler triple and vector triple product ?

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Q: Verify the parallelogram law for vectors u and v in R": |u + v|l? + ||u – v||° = 2||u||? + 2||v||?

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Q: If r is equal to 300 mm, Find: 1.) Rectangular form of r in ft 2.) Unit vector of r

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Q: Let A and B be nonzero vectors and let C = ||B||A+ ||A||B . Show that the measure of the angle…

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Q: If the volume of the parallelepiped determined by the vectors d, b, čeR' is a cubic units, which of…

A: Given, 2a→∧b→∧b→∧c→ Let, 2a→∧b→=u→ Now simplifying the given equation by apply the vector dot…

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: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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

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Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

Q: Which polygon is the result of reflecting polygon 1 through AB, then translating the reflected…

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Q: The volume of the parallelepiped determined by the vectors a =,b= and c = is: %3D (A) 12 (B) 6 (C)…

A: This question is related to volume of parallelepiped, we will solve it by using the formula of…

Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

Q: Show that LM = 2AB.

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Q: Given the vectors v =i+ 3j – 2k and w= 3i – 4j + k. Find the area of the parallelogram with sides…

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Q: The volume of the parallelepiped determined by the vectors ä =,b = and č = is: (A) 12 (B) 6 (C) 24…

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Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB