(a) Find the value of p so that the vectors i+2j+k and i+j+ pk are perpendicular. Find the cosine of the angle between the vectors 2i+j+k and i-j-2k. Hence, find the length of projection of 2i+j+k on i-j-2k . (b) (c) If a = i+2j-k and b = j+k, find a unit vector perpendicular to both a and b.

Q: Find the length of the vectors (a) 2i⃗ +3j⃗ −k⃗

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 14i V=-7i

A: To find Angle between two vector a→,b→ we use, cos α =  a→·b→|a→|·|b→|

Q: a) Find equation of the Line through point (2,3,0) perpendicular to the vectors U1 = i+2j+ 3k and U…

A: Line through point (2, 3,0)  Which perpendicular to U1 and U2

Q: The vectors A 5i + 7j – 8k and B 3i + yj + zk are known to be parallel. Find y and 2 y = = Z

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Q: Find the cosine of the angle between the vectors: a = 4i + 2j-k b=2i+ 4j-k

A: Simply take the dot/scalar product of both vectors a & b.

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Find the B-coordinate vectors of ei and e2, where and B : %3D %3D %3|

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Q: 7. i and y are vectors of magnitude 1 and 2, respectively, with an angle of 120° between them.…

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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: Find the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

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Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k b. u = 2i – 2j + k, v= 3i + 4k а.…

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Q: 2. The two unit vectors parallel to the line 3x + 4y = 1 are and 3. The two unit vectors…

A: 2) The line is 3x+4y=1. Rewrite the equation of the line in the slope intercept form as,…

Q: b) Consider the vectors a = 3i - 2j+7 K, and b = -5i +4j-3k, find 1-a.b 2- Angle between a and b. 3-…

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Q: In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to…

A: V=v1+v2  (Given)when two vector v1 & w are parellelthen the angle between v1 &w is 0° or…

Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

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Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OÁ = 2i + 5k,…

A: (a) Given that position Vectors, OA→=2i+5kOB→=3i+2j+3kOC→=i+j+k   As we know that, two vectors are…

Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

Q: Find cos(0) if 0 is the angle between the vectors u = 4i – 3k and v = 2i – 2j + k

A: Given,           u=4i+3k           v=2i-2j+k

Q: Find the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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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: In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 12i + 6j, V = -13i…

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Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +…

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by:…

Q: 1. The two unit vectors parallel to the line y = x- 3 are and

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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…

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Q: For a vector of my oriented at 245 degrees on the hexagonal system, find the projections of this…

A: We have to find the projection of the hexagonal system on the six leads.

Q: Find cos 0, where 0 is the angle between two vectors a = 2i – 3j + 2k, b = -2i + 2j+6k

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Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k ; 11+5/-6k dw (C): If w = tan x and…

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Q: Find the angle between the vectors a 0 = and b = 2i+j - 4k. 10i - j - 5k

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Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: 1. The two unit vectors parallel to the line y = 2x 1 are | and 2. The two unit vectors parallel to…

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a –…

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Q: The vectors v = (3, 4) is projected onto the x-axis The length of the projection is %3D A/

A: We have to find

Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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Q: Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular…

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Q: 4. Find the resultant using (a) the head-to-tail method, and (b) by summing up components. For the…

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Q: 1. Find the angle between two vectors u = i-2j - 2k and v= 6i + 3j+2k.

A: Given two vectors u→=i-2j-2k and v→=6i+3j+2k. Here find the angle between two vectors.

Q: 2. For the vectors (1, 1) and =(-1,1) Find the dot product u · v, and the angle 0 between the two…

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Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

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

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

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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: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k 41 +5/-6k i (C): If w = tan x and…

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Q: Find the angle 0 between the vectors a = 8i – j– 4k and b = 2i+j- 9k. %3D

A: A vector is a mathematical concept with both magnitude and direction. It's used to describe things…