2. a. Find a vector and unit vector perpendicular to each of the vector à + B and Å – B , where Å = ai + 4j + bk & B = 6k + i + 2j (Hint: a: 3 and b :0

Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: 3. In the above problem, what is, ĮD|, the magnitude of vector Ď = Ä – B ? (A) 1.0 cm (B) 1.1 cm (C)…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: 8 Find a vector of length: (2) (+) 3 a 10 units which is perpendicular to (a -4 b 3/2 units which is…

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Q: If a = i+ 2j +k and b = i+10j + k, find a unit vector with positive first coordinate orthogonal to…

A: The vectors are given as , a→=i^+2j^+k^ and b→=i^+10j^+k^ find a unit vector with positive first…

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

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

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Q: For AABC, let b and c denote the vector AB and AC , respectively. The vector BH is orthogonal to AC.…

A: Orthonormal vectors are perpendicular to each other.

Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: For what value of t, if any, is the vector (2, -4t) paralel to the vector (4, -1) ? t O A -2 %3D 1…

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Q: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

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Q: Find the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

Q: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

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Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

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 vector ū which satisfies the given conditions. i =, Ju| = 2 , ū and i have opposite…

A: The unit vector,  , in the direction of the vector is calculated as follows.

Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: 4. [6.1] If vector b is shown below, sketch a vector. a) Equal to b b) Opposite to b c) With the…

A: Solution of given question is written in below steps.

Q: 3. Use the given rectangular prism to state a single vector that is equivalent to a) BC + GH A B D E…

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Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

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Q: The unit vector which is perpendicular to both r1=8ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: Given That: The unit vector is perpendicular to r1=8ax+3ay-2az & r2=2ax+7ay-6az

Q: 16. Consider this regular octagon. If AB =d and BC =v, express each %3D vector in terms of u and v.…

A: Considering OD on x-axis. Angle at center O made by any side of regular octagon is 45degrees.

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: If A is a conutant vector and R= 3xi+ 3yj+ 32K, then grad (3A -R) = ? %3D A O 3A ©9A 27 A

A: A is a constant vector  R=3xi+3yj+3zk 3AR=9Axi+9Ayj+9Azk To find grad(3AR) Let Φ=9Ax+9Ay+9Az gradΦ=i…

Q: If a = i+ 10j + k and b = i+ 11j+ k, find a unit vector with positive first coordinate orthogonal to…

A: Vector cross product of given two vector  is orthogonal to two given vector

Q: Let b be a vector in Rm satisfying the following equation. 8 b -5 Then m = and b =

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Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

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Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

Q: 16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C…

A: 1)from the triangle law of addition  when two vectors are moving one by another then the third…

Q: Q2/ If A=ai+bj+3k, B= 2i+3j+4k, C-i+j+6k are vectors , perpendicular to B and A is perpendicular to…

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Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

Q: A line L has a direction vector v = 2i t 4j+ v5k and passes through the Find the distance between…

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Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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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: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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

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Q: If a = i+ 3j + k and b = i+9j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Find the sauare of the magnitude of the vector w =u + 2v if u = (8, 2,0) and V = (-1, 1, 2) |wf =…

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Q: 2. Given the figure below, find a single vector that is equivalent to C B tw b) 10 14 וד --(A-F+C) G…

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Q: If A = 3i + 4j and B = 7i + 24j, the %3D vector having the same magnitude as B and parallel to A is…

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Q: Assuming vector B is 12 units long, vector 4B is:

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