Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j, w=i-2j

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

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Q: Decompose v into two vectors,one parallel to w and the other orthogonal to w. ; v=-i+2j; w=3i-j

A: Given: Decompose v into two vectors,one parallel to w and the other orthogonal to w.  v=-i+2j;…

Q: Find a unit vector orthogonal to both u and v. u = 8i – 16j + 2k v = 16i + 32j – 6k -

A: In the given question we have to find the unit vector orthogonal to both u and v. u=8i-16j+2k…

Q: Find two vectors in opposite directions that are orthogonal to the vector        u = −(1/4)i + (3/2)…

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Q: Verify the Pythagorean Theorem for the vectors u and v.u = (3, −2), v = (4, 6)

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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: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

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

A: a.)u=2i+j , v=i+2j-klet θ be the angle between the…

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

A: Given the vectors u→=3i→+5j→+2k→, v→=12i→-34j→+110k→. To find: A unit vector orthogonal to both u→…

Q: Find the vectors u + v, u-v, and 5u | u = i + j, v = -j – 2k %3D u + v = u - v = 5u

A: The given vectors are

Q: Express the vector t as a linear combination of the vectors u, v, and w. 1 - 2 4 t = 0 , u = 5 , v =…

A: We use the definition of the linear combination of vectors to answer the given question.

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

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Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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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: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

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

A: Angle between two vectors, θ=cos-1u→.v→|u→| |v|→ a)  u→.v→=2i+j.i+2j-k       =2+2 u→.v→=4 |u→|=22+12…

Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Decompose v into two vectors,one parallel to w and the other orthogonal to w. v = 2i + j; w =4i + 3j

A: we have to decompose v into two vectors, one parallel to w and the other orthogonal to w. v = 2i +…

Q: 5.) Write the vector u=i+3j as the sum of two orthogonal vectors, one of which is in the direction…

A: Given vectors are: u=i+3jv=2i+5j

Q: Find b so that the vectors v = i + jand w = i + bj are orthogonal.

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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: Find two linearly independent vectors perpendicular to the vector V = 3 -5

A: Let's find.

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: Find a vector orthogonal to both given vectors u and v . u=2i-3j +k  v= -3i +4 j +4k

A: Given, u=2i-3j +k  v= -3i +4 j +4k    We have to find the orthogonal vector to both given vectors u…

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 of the given vectors and then we have to decompose v into two vectors, v1 and…

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

A: Given  u = i - 2j +2k = < 1, -2, 2 >v = 2i - j - 2k = < 2, -1, -2 >

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: 14. Find a vector perpendicular to both of the vectors * (ũ + v) and (ũ – v) where ủ = 2i – j + k,…

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Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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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: Find a unit vector orthogonal to both u and v. u = i + 2j v = i+ 3k

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Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: i +j +k andi – j -k.

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

Q: Find three mutually orthogonal unit vectors in ℝ3 besides ±i, ±j, and ±k.

A: Vector: At first we can take a=<1,1,1> The second case we can take b=<0,1,-1> The…

Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w -x-y+ 3z 5w + 2x +…

A: In the question it is asked to write the vector for the given equations. w-x-y-3z=05w+2x+y+3z=0 AS…

Q: 3. Find two unit vectors orthogonal to both j − k and i + j

A: We will find the two unit vectors orthogonal to j-k and I+j as following.

Q: Find a unit Vector orthogonal to both vectors: U =21 +5j-K and V=i+3j-2K.

A: We can find the unit vector as below

Q: Find the angle between the vectors. 20 u= - 5 531-Si and v= zi-[2 V3= 2i:

A: The given vectors are

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

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Q: Find a unit vector orthogonal to both u and v. u = i + 2j + 2k v = 2i +j – 2k

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Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: State whether the vectors are parallel, orthogonal, or neither. 5) v = 2i + j, w =i- 2j 6) v = 2i +…

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

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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: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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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 =…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.