9) If v = 5i + j and w 2i + j, find v + w . Find the quantity if v = 5i - 7j and w = 3i + 2j. 10) | - |W Find the unit vector having the same direction as v. 11) v = -4i - 3j

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

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: I\ Find the unit vector that has the same direction as vector v = -4i - 3j + 6k ? %3D

A:

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

Q: a/Find the length and diredtion of the vector 式ド、で Aュ2i+3k where や ノ

A: The given question is from vector and can be solved as shown in step2

Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find a unit vector that has the same direction as the given vector. 4i - j+ 8k

A: Unit vector means the vector whose magnitude is equal to one. So to find the unit vector in the…

Q: If a = 3i +j - 2k and b = 5i –j- 2k, then find %3D а. а xb b. vector resolute of vector a in…

A: We will find out the required values.

Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

A:

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

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: Given, X = -i + 3j  and Y = 4i -2j + 2k

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

A:

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Let b be the vector of length 35 that when drawn in standard position makes a 290° angle with the…

A: Given : length of vector b=35 ⇒b=35 Also, b makes angle 290° with positive x axis. So, b=b1i+b2j,…

Q: Show that the points with position vectors 3i−5j, 4i+j, 6i+13j are collinear. If the point whose…

A:

Q: The vector which has length 2 and direction opposite to u?

A: We have the given vector as u=-122   We have to find a vector that has length 2 and direction…

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: 6. Find the unit vector that has the same direction as the vector v = 3i- 2j

A:

Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

A:

Q: 6. For the vectors ü = (4, 3) and i= (-2, 3), caleulate the following quantities. (a) la+ 레 (b) la+…

A:

Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

A:

Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

A:

Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

A:

Q: Find a unit vector that has the same direction as  4i − j + 8k.

A: we have to find a unit vector that has the same direction as 4i-j+8k let the given vector be a→…

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

Q: o v based at the origin.

A: Sketch the vector v = (2, −3) based at P = (1, 4) and the vector v0 equivalent to v based at the…

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

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

A: Follow the procedure given below.

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

Q: Which vector has the smaller magnitude: u = 3i - j - k or v = 2(i + j + k)?

A: Our Aim is to tell which vector given below has the smaller magnitude u⇀=3i-j-k and v⇀=2i+2j+2k.

Q: Find a unit vector in the same direction as (2i - 6j - k). Oi-j-k O

A:

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

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

A:

Q: Parametrize the line that passes through the point (1, 2, 3) rallel to the vector V = -3i +7k .

A:

Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

A:

Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

A:

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

A:

Q: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

A: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

Q: IF: A = 2i - j+2k and B=9i+20j + 12k Find: Unit vector for A direction. Unit vector for B direction.…

A:

Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Two out-of-phase alternating voltages are represented by: = 3.4sin (wt +) and V, = 1.3cos (wt +).…

A: we will find horizontal and vertical component of each voltage and then represent them in vector…

Q: Express the vector v = 4i + 2j - k in terms of magnitude and %3D direction.

A: