Find the component of V, |V|= V5 in the direction of a vector from A(0,0, 4) to B(2,5, 0).

Q: Find a unit vector that is orthogonal to both u = i − 4j + k and v = 2i + 3j.

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Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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

A: Sol

Q: Let v be the vector from initial point P1 = (2, -5) to terminal point P2 = (-6, 6). Write v in terms…

A: Given, The initial point is P1 = (2, -5) to terminal point P2 = (-6, 6).

Q: Let v be the vector from initial point P1 = (-7, -4),to terminal point P2 = (0, -2). Write v in…

A: Vector u from (a,b) to (c,d) is (c-a,d-b) or  (c-a)i+(d-b)j

Q: Find a vector v parallel to the intersection of the planes - (2x + 4y + 3z) = 4 and 3x + y + z = 7.

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Q: Let v be the vector from initial point P1 = (-1, 3) to terminal point P2 = (2, 7). Write v in terms…

A: Given : the two points are given as P1=-1,3 and P2=2,7 To find: a vector v from initial point P1 to…

Q: Let v be the vector from initial point P1 = (4, -5), to terminal point P2 = (4, 3). Write v in terms…

A: Let v be the vector from initial point P1 = (4, -5), to terminal point P2 = (4, 3). To write v in…

Q: Find a unit vector u in the direction of the vector from P1(1, 0, 1) to P2(3, 2, 0).

A: Concept: Unit vector is a quantity which has a magnitude as 1and as well as direction, it is also…

Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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Q: Find the coordinate vector of w relative to the basis S = {u1, u2 } for R2 u1 = (9, – 9), uz = (3,…

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Q: Find a unit vector in the direction of vector (v= ai + bj ) and orthogonal to the vector ( u= 3i -…

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Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

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Q: Let v be the vector from initial point P1 = (-7, -4) to terminal point P2 = (0, -2). Write v in…

A: To write the vector v in terms of i and j.

Q: products

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Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

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Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: Find a unit vector orthogonal to both u and v. u = 31 - 2j - 5k V = +

A: Given: The given vectors are: u=3i-2j-5kv=12i-34j+110k To find: Unit vector orthogonal to both u and…

Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

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Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Let v be the vector from initial point P1 = (-4, -4),to terminal point P2 = (6, 2). Write v in terms…

A: Initial point is P1=-4, -4 & terminal point is P2=6, 2.

Q: Find the unit vector u in the direction of the vector v=4(2, 1, 2).

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Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: Let v be the vector from initial point P1 = (-3, 0) to terminal point P2 = (-2, -2). Write v in…

A: Solution:- we have to find vector v in which  initial point P1 = (-3, 0) to terminal point P2 = (-2,…

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

A: By definition, Any vector is said to be irrotational if the curl of the vector is zero. The given…

Q: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

A: u=-3i+2j-5k,  v=i-j+4k Now the vector orthogonal to both u and v is, w=u×v=…

Q: Let v be the vector from initial point P1 = (4, -5) to terminal point P2 = (4, 3). Write v in terms…

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Q: Find two linearly independent vectors perpendicular to the vector i = |3

A: to find linearly independent vector perpendicular to vector v→=139 solution let X=x1x2x3 as we know,…

Q: Find a unit vector u in the direction of the given vector. (- 1,2)

A: The given vector is, < -1, 2 >.

Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient

Q: Let v be the vector from initial point P, to terminal point P,. Write v in terms of i and j. P1 =…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector