Let å = and b= 3 a) Find the area of the parallelogram formed by the two vectors. b) If the two vectors are direction vectors of two lines passing Q(2, –2,1), find the scalar equation of the plane which contains the two lines.

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

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: 3. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i…

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

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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: 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: Find the area of the parallelogram determined by the vectors u and v.

A: Given any non-zero vectors.

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

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Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

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: Show that the vector v = [a, b, c]* is perpendicular to the plane P with equation ax + by + cz + d =…

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Q: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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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: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

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Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: Given a vector A = 3a, - 2a, - 16a, find its components normal to the plane 2x + 2y – z + 8 = 0 and…

A: We have to determine component normal to the plane

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Q: Find the equation for the plane through the point Po = (3,4,3) and normal to the vector n=21 + 7j +…

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Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

A: First we have to find the angle between the vectors v and w where v=i-2j+k and w=i+j-2k. For this,…

Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

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Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Determine a unit vector perpendicular to the plane a =21-6j –3k and b=4i+3j – *

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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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: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: Show that the vectors u=, v= , and w= satisfy the following properties of the cross product. и хи30…

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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: 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: 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: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: The volume of parallelepiped determined by the vectors u = 2i – k, v = 2j – 3k and .= w = i + j+k is…

A: We use the definition of the volume of a parallelopiped determined by the vectors a, b and c to find…

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: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = i − j + k, v = i + k

A: Given vectorsu = i-j+k , v = i+kArea of parallelogram is equal to u x v

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A: Given that position vector of A and B with respect to the origin O are a and b respectively. M is…

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…

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Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

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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: 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:…