Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose position vector is 5aj + 7aj is also on the line, find the value of a.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

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: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b,…

A: Given that P , Q & R lie on a straight line. It means vectors are coplanar . since if vectors…

Q: The position vectors of points A, B and C are OÃ = 2i – j + nk , OB =ỉ+3j – 2K and OC = -i – mỉ – 3k…

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Q: Given initial point  P1 = (−2, 1)  and terminal point  P2 = (5, 4),  write the vector v in terms…

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Q: The position vectors of points A, B and C are OA = 21 -j + nk , OB=i+ 3j – 2k and OC = -i - mj – 3k…

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Q: For what value of m, the vector 4i + 2j – 3k and mi - j+ 3k have same magnitude? Given the points A…

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Q: Find the direction vector of the line joining the points (a) A(7, 6) and B(-2,5), (b) with position…

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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…

A: Consider the vectors: a=i+j+k……1b=2i+3j……2c=3i+5j-2k……3d=k-j……4

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: Given vectors u = 2xi + 9j and v = xi - 4j, find x so that u and v are orthogonal.

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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: 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: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Given that a =-i+j+k, b3D2i+j-4k and c= 3i-5j+k, find a vector in the direction as (-a+3b-c) and has…

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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: Suppose u = (-1.8,-2.1) and v = . Find the angle between the two (position) vectors u and v. Provide…

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Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

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: Given a vector à = 3a, + 2a, – 6as , determine the vector component of à tangential to the cone. O…

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Q: Consider the points P(2,7) and Q(6, 4). Write PQ as a product of its magnitude and a unit vector in…

A: Given points are P(2, 7) and Q(6, 4).

Q: Prove that the points with position vectors a+2b, 2a−b and 3a−4b are collinear.

A: We have to use determinant method to solve.

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

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 –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Given the vectors a=(-1,5,-4) and b=(2,-7,2) find the vectors x € R3 , with magnitude v371 and…

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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: The plane that contains the point (3, –1, -4) and the line with equation y – 1= 3z is orthogonal to…

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

A: The position vectors of the points which are collinear is: 10i+3j ,     12i-5j ,      ai+11j

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

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

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Q: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

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: The line / passes through the points with position vectors 2i – 3j + 5k and 7j + k. Given the point…

A: Given points are (2,-3,5) and (0,7,1)  So the direction ratio of the line= (2,-3,5) - (0,7,1)=…

Q: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Give the vector equation of the line passing through P and Q

A: Consider the points: P=1, -2Q=3, 0

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…

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 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: A line L has a direction vector v = 2i t 4j+ v5k and passes through the Find the distance between…

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Q: Define the points P(1,1) and Q(3,-4). Carry out the following calculation. Find two vectors parallel…

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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: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

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: value

A: If, P, Q & R are collinear, then,  The position vector of QP is, The position vector of P - the…

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.