Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k W=-2i+8j-6k w=2i+8j+6k

Q: snip

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Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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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: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Use the vector u= -1i -4j , v= -9i + 7j and w= 7i + 1j to find the following. u+ (v- w) = %3D i+ j.

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Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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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 the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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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 the angle between the vector u = i−2j + 2k and (a) v = −3i + 6j + 2k (b) w = 2i + 7j + 6k (c) z…

A: Given That: The vectors, u = i - 2j +2k v = -3i+6j+2k w = 2i+7j+6k z = -3i+6j-6k

Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

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Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

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 the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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

Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar 4u - (2v - w)

A: Given: u=-2i+3j , v=6i-j , w=-3i

Q: Find a unit vector orthogonal to both u and v. u = 8i - 16j + 4k v = 16i + 32j – 12k

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Q: find the sum of vector AB and CD where A (1,-1) B (2,0) C(-,3) D(-2,2)

A: Let A (1,-1) B (2,0) C(-1,3) D(-2,2) be the given vector. Of course here in the problem   "-1"is…

Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

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Q: Find u + v, u – v, and 4u - 5v. Then sketch each resultant vector. u = 5i, v = j (a) u + v u + v = y…

A: the given vectors are: u=5i v=j we have to find: a) u+v b) u-v c) 4u-5v then we have to sketch the…

Q: Find a vector that is perpendicular to both and 2. A =-i - 2j +4k B = 4i - j

A: Take cross product and it's magnitude then find unit vector in perpendicular to both vector

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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Q: Determine whether the vectors a = 2i-3j+ 5k, b 3i+j-2k and c=i-7j+12k are linearly dependent or…

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

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: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

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

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Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: For the vectors u = (- 1,3) and v= (-4,2), calculate proj,u and scal,u. proj, u = D

A: Vector and scalar projection

Q: Write the vector v= 1 as the linear combination of vectors --0 w =

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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 vector joining the points P1= (-3, 1) and P2= (5, 2) %3D %3D in terms of i and j.

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Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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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: 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: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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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,…