The vectors A and B are given by A = 2î + 3j and B = - î + 2j. (A) Determine the scalar product A · B. (B) Find the angle 0 between A and B.

Q: Find the angle between the vector through the origin & the point (1,1,1) and the component of Ā = 2i…

A: Given:-A vector passes through the origin & the point (1,1,1) A→=2i+2j-k and B→=i+j To Find:-The…

Q: The vectors a(3;-4) and b(x; 9) are perpendicular to each other. Calculate the magnitude of the…

A: Given vectors are: a→=3,4 and b→=x,9

Q: a) Let a = 2i – 3j + xk and b = -3i + j + xk. Find the values of x for which vectors a and b are at…

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Q: Given the vector ū = - 4i + 5j, find the magnitude and angle in which the vector points (measured…

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Q: On the diagram to the right, what are the components of the resultant of the three vectors shown? *…

A: We have three vectors, two of them are in horizontal direction, 6 N is -x direction and  14 N in +x…

Q: (a) Find the vector of length 2 that makes an angle of π/4 with the positive x-axis. (b) Find the…

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Q: Find the angle between the vectors a = 10i – j – 5k - and b = 2i+j – 4k. Answer (in radians): 0 =

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Q: Calculate the force (in Newtons) required to push a 50kg wagon up a 0.2 radian inclined plane. One…

A: Solution:

Q: If a = 3i +j - 2k and b = 5i –j- 2k, then find %3D а. а xb b. vector resolute of vector a in…

A: We will find out the required values.

Q: In the figure, a vector a→ with a magnitude of 24.1 m is directed at angle θ = 68o counterclockwise…

A: Given that: Magnitude of a→ =24.1mAngle of a→ w.r.t. coordinate axes: θ=68°Angle of primed…

Q: use the vectors v=-2i+j and w=4i+3j to find: Find a unit vector in the opposite direction of w.

A: Given vectors are v=-2i+j , w=4i+3j

Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

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Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Find the unit vector in the same direction as v = 4i - 3j. Then verify that the vector has magnitude…

A: Consider the following vector: v→=4i^-3j^ Consider the following formula: unit…

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: nd the unit vector 3i - 4j+ 5k perpendicular to the vectors: 4i + 5j-6k

A: Let the given vectors be  u→=3i-4j+5kv→=4i+5j-6k we have to find the unit vector perpendicular to…

Q: Find the unit vector in the same direction as v = 2i - 3j -6k

A: Given vector is v=2i-3j-6k. To find the unit vector in the same direction of the given vector.…

Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

Q: What is the unit vector with the same direction as the vector v = 2i - 7j? Write as a linear…

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Q: Let x→=2i→−12j→+k→ and y→=12i→+2j→+3k→ be the two vectors. Find the angle (in radians) between the…

A: Given two vectors are To find angle between given two vectors.

Q: Calculate the cosine of the angle which the vector 2i+2j-k makes with the positive x-axis

A: Given: find the cosine of the angle which the vector 2i+2j-k makes with positive x axis

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

A: Solution is given below:

Q: Find the angle between the vector through the origin & the point (1,1,1) and the component of Ā = 2i…

A:

Q: Determine a unit vector perpendicular to both A=i+2j-3k and B=-2i-3j+k

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

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

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Q: Express the vector - 4i - 8j + k as a product of its length and direction. - 4i - 8j + k=[Di+ ()j+…

A: To express the vector -4i-8j+k as a product of its length and direction.

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: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: nd the an

A: Here we have, u→=cosπ3i+sinπ3j ........................................ (1)  v→=cos3π4i+sin3π4j…

Q: Find the angle O between the vectorS 3. and -2

A: Given: 34-2 &114 We can write given vectors as, u=3, 4, -2v=1, 1, 4 We know that,…

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. √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 magnitude of the vector y = 2i-2i. v =

A: Given,           v=2i-2j

Q: 13. Find the unit vector having the same direction as v. v = 6i-8j

A: We have to find the unit vector.

Q: The vectors 2 and are given by 1= 21+4j-k m and --3i+5k m. Detemine the scalar and vector product à…

A: on solving this we get

Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k

Q: Sketch the vector v = 3i - 3j and find its magnitude.

A: v=3i-3j The graph is,

Q: 2. Find an unit vector perpendicular on both a =i +2]- and 6 2i -k.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

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

A: here here we have

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 the same direction as  i + j  whose component in the   direction of  2i-2k  is…

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Q: Find the angle a between the vectors 日- 2 and a =

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Q: Find the dot product of the vectors v = 5i - 3j and w = 2i - j.

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Q: Find the unit vector in the same direction as v = 5i - 12j. Then verify that thevector has magnitude…

A: Unit vector in same direction vectorvector's magnitude

Q: Which is traveling faster, a car whose velocity vector is 27i⃗ +32j⃗ , or a car whose velocity…

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Q: Find the angle between the vectors u = - 5i – 3j and v = 6i + 2j + 5k.

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Q: Determine a unit vector perpendicular to the both vectors A - 5i + 6j – 8k and B : - 2i + 5k. |0| =…

A: