Given that ? = (5,4,0) ??? ? = (−1,4, −3) , find the unit vector along the direction of a vector  has P as initial point and Q as a terminal point

Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: 27. Find a unit vector that is orthogonal to both i +j and i+ k.

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Q: Write the following vector as a linear combination of the unit vectors i and j. (-4,Radical 2)

A: We need to the following vector as a linear combination of the unit vectors i and j

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: (A) Find the vector that is Normal to: A = 2i + 3j +k and such that it is lies in the plane…

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Q: Find the unit vector in the same direction as the vector u = [2, –1, –9]. Ex: 1.234 C Ex: 1.234 Ex:…

A: We will find the modulus (norm) of the vector and divide the vector by the norm to find the unit…

Q: Determine a unit vector perpendicular to the both vectors A : 2i + 5j – 4k and B - 3i + 6k. |0| = (…

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Q: or what value of t , if any, is the vector (2t, 1) parallel to the vector (4, -1) t =-2 DA. t = 2…

A: Given that vector 2t,1 paralle to the vector 4,-1find t

Q: For what value of t, if any, is the vector (8t, 2) parallel to the vector (4, -1) ?

A: Given vectors:A= <8t, 2> and  B= <4, -1>

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Given a vector with initial point at P1 and terminal point at P2 given below, find an equivalent…

A: (2,-1) and (3,2)

Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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Q: The U is a unit vector in the direction of (2, 3). Select one: True O False

A: If magnitude is 1 then given vector is unit vector

Q: Find the magnitude of the vector and the angle 6,0° <0<360°, that the vector makes with the positive…

A:

Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = &lt;1, 2, 3&gt; v = &lt;2, 2, -1&gt; w = &lt;4, 0, -4&gt;

Q: Find a vector and unit vector perpendicular to each of the vector A + B and A – B,

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Q: For what value of t,if any, is the vector (1, 4t) parallel to the vector (4, - 1)? Not OA. t = -2…

A: If the Vectors u and v are parallel then u=kV , K is any scalar.

Q: Given: f(x, y) = 3x² – 2y² at (-,0) in the direction from P(-,0) to Q(0,1). . What is the unit…

A: The given problem is to find unit vector of the function in which direction from point P(-3/4,0) to…

Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Express the vector v = (3,2,7) as a sum…

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Q: Find the given vector. The unit vector in the direction of u =〈1, 0, 7〉

A: A unit vector gets its name from the fact that the magnitude of the unit vector is unity or 1. It is…

Q: Q3. Prove that (only one): Ĝ = ax-ay is a unit vector? a- b- L = 6ax – 3a, + 2a, and M = 3a, + 2a, –…

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Q: Find the magnitude of the vector a and the smallest positive angle 0 from the positive x-axis to the…

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Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: In Cª, find a unit vector ū that is a positive real number multiple of z = (1 – i, i, 2, 3+ 4i).

A: Introduction: For a given complex vector z=z1,z2,...,zn, its length is formulated as…

Q: Find the direction of the resultant vector. (8, 10) V (7,-1) W [?]° 1>13

A: The given data is: v→=8i+10jw→=7i-j  To find the direction of the resultant vector.

Q: Find a vector that is perpendicular to both and 2. A =-i - 2j +4k B = 4i - j

A: Take cross product and it's magnitude then find unit vector in perpendicular to both vector

Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: Find the length of the vector. v= (4, 3) M -| 43

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Q: = - A. Find the unit vector that makes an angle (0 with the positive x-axis.

A: The unit vector makes an angle θ=-3π4 with positive x-axis

Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: 10. Find the unit vector in the direction of u=2i+3j-k

A: Magnitude of u = sqrt (u1^2 + u2^2 + u3^2)   Unit vector direction of d =&gt; u/ (Magnitude of u)…

Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: Let v = -4i + 3j. Find a vector that is half the length and points in the same direction as V

A: Given vector v=-4i+3j. To find: A vector  that is half the length and points in the same direction…

Q: Find a vector equation with parameter ?t for the line through the point (8,0,−5) and parallel to the…

A: Given,           The line through the point (8,0,−5) and parallel to the vector 2i−3j+3k

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: Find the magnitude of the vector AB A=(0, 7) and B(-24,0)

A: Given : A = (0, 7) and B = (-24, 0)   To find the magnitude of the vector AB.

Q: Find a unit vector e, where v = (4,2, 5) ey = %3D

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Q: Find the angle 0 between the vectors i + 2j - 3k and -i + 2j + k.

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Q: Given a vector v with initial point P(5,12) and terminal point Q(−2,−12), write the vector in terms…

A: vector with initial p1,p2 and                 terminal (q1,q2)is given by v=&lt;q1-p1,q2-p2&gt;

Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: What is the magnitude of the Vector PQ. P=(1,11) and Q= (9,3)

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Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

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Q: Given the vectors a = (−2, −5, −3) and b = (1, −4, 2), find A unit vector in the direction of a.

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Q: / Let v = -4i + 3j. Find a vector that is half the length and points in the same direction as v

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Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

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