1. Given two vectors P= ai+ bi + ck where a, b,c represent the last three digits of your index number and Q=-3i - 5j+4k. {Index number = (********028)} Calculate the following:- i) ii) angle 0, the angle between vectors P and Q using the dot product formula.

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

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Q: or what values of aj are the vectors [ai,4,3] and a) orthogonal? b) Parallel? c) Have 45 degree…

A: If 2 vectors a⇀,b⇀  are orthogonal, their dot product a⇀.b⇀ =0 Let u=a1,4,3 and v= 3,-2,12 So,…

Q: Find the area of the parallelogram that has the vectors as adjacent sides. AB= 6i + 6j - 6k, AD = 6i…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are find the cross product

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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

A: The equation of the line, PQ passing through the points P and Q is defined as follows.…

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: If A : li + 4j – 8k, B = -6i + 5j + 6k, C 9, and C is perpendicular to both A and B, write the C in…

A: Given, A→=i^+4j^-8k^B→=-6i^+5j^+6k^ Let, the required C→ vector be, C→=c1i^+c2j^+c3k^.......(1)

Q: Find the angle between the vectors u = ⟨3, 1⟩, v = ⟨2, −1⟩     (a) in radians and (b) in degrees.

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Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: What is the cross product of the vectorS 2i + 3j + k and 61 + 9j + 3k? Explain why your answer is…

A: Cross Product: Cross product of two vectors is the method of multiplication of two vectors. A cross…

Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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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: What is the cCToss product of the vectors 2i + 3j + k and 6i + 9j + 3k? Explain why your answer is…

A: Given vectors are P=2i+3j+k and Q=6i+9j+3k

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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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: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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

A: Given,

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: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

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

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Q: Find all unit vectors perpendicular to (3,1,4) that make equal angles with j and k.

A: Here we have to find the all unit vectors perpendicular to (3,1,4) that make equal angles with j and…

Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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Q: Find two unit vectors in 2-space that make an angle of 45° with 10i +3, NOTE: Enter the exact…

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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: 2. Draw a figure to illustrate part of the infinite pattern that can be derived from a given…

A: Given data is: Draw a figure to illustrate the part of infinite pattern that can derived from…

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

A: Solution is given below:

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

A: NOTE: Refresh your page if you can't see any equations. . the given vector is  find the norm

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: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

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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: 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: Given two vectors a = (−2, 1, 3) and b = (3, −1, 2), does c = (−18, 7, 1) lie on the plane…

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Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

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 u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

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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: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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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 answers…

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Q: Find the measure of the angle between the two vectors. 24) u-(9,9) v-(-8,-5) V =

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Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

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Q: Determine the angle, to the nearest degree, between the vectors = (5,3), b= (-1,–2)

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Q: value

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

Q: The position vectors of points A, B and C are given as OA = 4i + j-3k , OB = 7i+3j-5k and OC =…

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Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

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Q: 4. Find a unit vector that is perpendicular (5, 6). to

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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.