Q1. A- Find the cross product (uxv) of vector (u = i – 2j + 5k) and vector ( v=< 3,-6,15 >). Are the two vectors parallel or normal to each other? B. Find a vector has length 10 in the direction of vector V=< 3,-6,15 >.

Q: 3. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i…

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Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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Q: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other vector…

Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

Q: 3. Given the vector ā = (x, y,=), where x = 0, y = 2 and z = 8 . Find the vector b with magnitude of…

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Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

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Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Find the positive value for which the vector r(t) = (3t, 10t², 7t² – 2) is perpendicular to r'(t).

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Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

A: First we have to find the angle between the vectors v and w where v=i-2j+k and w=i+j-2k. For this,…

Q: Q2) if the vechrs V=-i +5 and ū=Tz i+5J+2 R Find a) The scalev component of ū in the divection of V…

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Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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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: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: To Determine: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w…

Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: • We have 2x 2y Vf(x, y, z) = i+ +1)j+6k. x² + y²- 1 x² + y? – 1 | Thus Vf(1,1,0) = 27 + 37 + 6K.

A: We have to show the steps for the above equation.

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: Find the cross product of the unit vectors. jx i

A: Topic :- Vector

Q: Q. For the Spheri cal polas Coozdinates (r0,d), prove that their unit vectors mutually orthogonal?…

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+fk where a = 3, b = -3, c =…

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Q: Q.5) Determine and what is the differences between the two results. Also prove that is orthogonal to…

A: We have to find the difference between the vectors A→=-i^+8j^+4k^ and B→=i^+18j^-6k^. Also, prove…

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: How does the cross product i x ì relate to the vectors ở and i geometrically? Use this to compute d…

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Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

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Q: Determine the i - component of the cross- product for the two vectors: x = ai+bj+ck and y = di+ej+fk…

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = i − j + k, v = i + k

A: Given vectorsu = i-j+k , v = i+kArea of parallelogram is equal to u x v

Q: (:) R de u = ve v = ( t2 ) for vectors, show = 2u1v1 + 3u2v2 is an internal product

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Q: Compute the distance between the following vectors: 2 2 w = 3 v = -4 1

A: Hope it is useful

Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Q when analyzing the vector Å-zi-j+3K To theSum Parallet to the ve ctor 3=i+2j+zk etwo vectors Lirst…

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Q: Q3. Prove that (only one): ax-V3ay a- is a unit vector? b- A = 6ax – 3a, + 2a, and B = 3ax + 2a,y –…

A: Given two statements . We need to prove only one out of that  So, here we will prove first statement…

Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

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: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

Q: Consider the lines 3 - z x – 5 l1 : 2 and I. Find two unit vectors that are parallel to l1.

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Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient