Find the vector w of length 4 in the direction of v = 7i + 4j. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.)

Q: Find a unit vector in the same direction as 8i-j+ 4K

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Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

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: Find a vector that has the same direction as 8i-j+4K but has a length of 6

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Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: Describe all unit vectors orthogonal to both of the given vectors. −4i + 6j − 2k,   5i + 4j + 9k

A: Concept: The cross product a x b is orthogonal to both the vectors a and ba = −4i + 6j − 2kb = 5i +…

Q: Find the unit vector of A=3ax+2ay-3az

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Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: sketch the vectors AB and PÓ, and determine whether they are equivalent. А %3 (1,4), В %3 (-6, 3),…

A: Given points are: A=1,4 ; B=-6,3 ; P=1,4 ; Q=6,3 We have to determine whether the vectors AB→ and…

Q: 4. Find a unit vector in the same direction as the vector 8i- j+ 4k.

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Q: Show that Il all = 11b|l Are the vectors ã' and b equal?

A: ||a|| = ||b|| a and b are not equal.

Q: Use scalar product to find the angle between the two vectors A = 2.00i + 3.00j + 1.00k B = - 4.00i +…

A: The given vectors are  A=2i+3j+1kB=-4i+2j-1k

Q: Find the magnitude of the vector. (-3, – 7)

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Q: Express the given vector in terms of the unit (о, -5, 7)

A: Given query is to express the vector inthe form of unit vector.

Q: 4) -16i + 30j

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Q: 1. Determine the dot product of the two vectors in the diagram.

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Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: Compute the following cross product. Then make a sketch showing the two vectors and their cross…

A: From the definition of the cross product, A×B=ijkabcdef=i(bf-ec)-j(af-cd)+k(ae-bd) If A = (-1)i +…

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: 5. Express the vector having magnitude 7, and direction 13 degrees (when drawn in standard…

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Q: Show that the vectors are orthogonal.

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Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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Q: Express the vectors in Exercises 13 and 14 in terms of their lengths and directions. 13. 2i - 3j +…

A: 13.Given vector is 2i - 3j + 6k.

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: Find the following vector. The vector in the direction of (24,10) with length 2

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Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

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

A: Solution is given below:

Q: Find the dot product of the given vectors ü=, ö=

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Q: Find a unit vector u in the direction opposite of (-8,-4,-3).

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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: Sketch the vectors

A: Solution : The magnitude  of |a| , |b|, |c| are  |a|=a1+a2|b|=b1+b2|c|=c1+c2 a=(-3)2+22     =9+4…

Q: determine the magnitude of the vector ∥⟨2,8⟩∥

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Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: Express the vectors in terms of their lengths anddirections. 2i - 3j + 6k

A: The given vector is a=2i-3j+6k. Compute the length of the vector as follows. a=22+-32+62=4+9+36=49=7…

Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: Find the unit vector in the direction of the given vector a, and express it using standard unit…

A: Find the unit vector in the direction of the given vector a . vector a = 20i - 21j  . Here i…

Q: Express the vectors in terms of their lengths anddirections. -i - j

A: Given vector is: v = -i -j Then we get, The magnitude or the length is: = sqrt{(-1)^2+(-1)^2} =…

Q: Given the vector A 2i +3 j, what is 3 A? Expand vector and collect like terms (simplify).

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Q: Find a vector orthogonal to the vectors and

A: This problem belongs to vector section and we solve this using dot product concept

Q: Determine the vector component of the vector 3i-4k on the vector 4j+3k.

A: Given two vectors are: a→=3i-4k                                    &    b→=4j+3k

Q: (B): Find the unit vector perpendicular to the vectors: 4i + 5j - 6k 3i - 4j+5k ;

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Q: Find the vector in v that has magnitude 8 and is in the opposite direction of (-3, –5, 1). v = help…

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Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: It is known that the unit vector along the direction v is given by vv. Since it is an unit vector,…

Q: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

A: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

Q: Find the given vector. Vector v of length 4 in the direction of = (-4, -4)

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Q: Resolve the vector a = -i+ 4j+9k into orthogonal vectors, one of which is parallel to b =i- 3j – k.

A: Given vectors are a→=−i^+4j^+9k^ and b→=i^−3j^−k^. Here, we using the concept of projection . We can…

Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1