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

Q: 12 If the position vectors of P and Q are i+3j- 7k and 5i - 2j + 4k respectively, find PQ and…

A: Since,you have posted multiple questions so according to our guidelines we will solve only first…

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

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Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

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Q: Determine the resultant of two vectors with magnitudes of 50 and 30 and an angle of 110 degrees…

A: let  A=50 & B=30, θ=1100 We know resultant between two vectors A→ & B→ when angle between…

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact…

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

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Q: Convert the vector Ả = = pzsino a,+ 3pcos¢ a p + pcosø sinø az to RCS. Simplify your answer and show…

A: A vector in cylindrical coordinates can be written as A→=Aρaρ⏞+Aφaϕ⏞+Azaz⏞ A vector in cartesian…

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: Consider the parallelogram given by vectors [12, 5], and [18, 0]. Give the lengths of the altitudes…

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Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 6j. NOTE: Enter the exact…

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Q: Find the cosine of the angle between the vectors: a = 4i + 2j-k b=2i+ 4j-k

A: Simply take the dot/scalar product of both vectors a & b.

Q: Find two unit vectors parallel to v = -2i + 5j – 3k.

A: Given:- v=-2i +5j-3k  To find:- Two units vectors parallel to given vector v

Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

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

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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: The points A, B, C and D form a parallelogram. The points A, B and C have position vectors 2i –…

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

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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: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: a)a→=-3 i + 8 jUnit vector as the same direction;u= a→a→ =(-3 i + 8 j)(-3)2+(8)2u=(-3 i + 8…

Q: 12. If the position vectors of P and Q are i + 3j-7k and 5i- 2j + 4k respectively, find PQ and…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer one question…

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: find the cosine of the angle between the vectors. (1, 1, 1), (2, −1, 2)

A: Given: (1, 1, 1), (2, −1, 2)

Q: Show that the pair of vectors is perpendicular. -2i - 5j and 10i – 4j To show that -2i – 5j and 10i…

A: Given,            To show that -2i -5j and 10i - 4j are perpendicular.

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 4j.

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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: What is the dot product of the vectors a = 4i + 3j and b = -3i + 4j?

A: Solution is given below:

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: Find the angle between the vectors r = (-1, 2) and s = (4, 2)

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Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: The angle between the vectors A = 2j -3j +1k and B = 4i -3j +1k, in term of cos@ is !!

A: We use the definition of angle between two vectors to find the angle between the vectors A and B.

Q: Express the vectors in terms of their lengths anddirections. √2i + √2j

A: If a vector is defined as: v→=ai+bj Then, the length or magnitude of the vector is: |v→|=a2+b2 The…

Q: Find the position vector of the point of intersection of the line joining the points whose position…

A: Given: The position vector of the points 5i^-4j^ and -3i^+4j^; -13i^+4j^ and -5i^+j^

Q: Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b help (vectors)

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Q: Find a unit vector in the same direction as (2i - 6j - k). Oi-j-k O

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Q: The angle between vectors A = 91-j+5k and B = (-2,7,1) is.. ******

A: According to our terms and conditions,we can only solve one problem at a time. So please repost the…

Q: If a vector v lies in the third quadrant and makes an angle n with the positivex - axis and…

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Q: If a = 3i – j +2k, b = I + 3j – 2k, determine the magnitude and direction cosine of the product…

A: Dot Product: Let u=u1i+u2j+u3k and v=v1i+v2j+v3k be two vectors. Then the dot product of u and v is…

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 4j. NOTE: Enter the exact…

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Q: If vector C is added to vector B , the result is -9i -8j . If vector B is subtracted from vector C,…

A: If vector C is added to vector B , the result is -9i-8j C+B=-9i-8j If vector B is subtracted from…

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: If a = 3i-j-4k, b - 2i + 4j-3k and c i+2j-k. Find unit vector parallel to 3 a -2 b +4 c. Q.1

A: Comment:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If a vector V is in standard position and the tip of the vector corresponds to the point(a, b), then…

A: Given, If a vector V is in standard position and the tip of the vector corresponds to the point(a,…

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: Perpendicular vectors are also said to be __________.

A: Perpendicular vectors are also said to be __________.

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.