RS || VT, RV 1 VT, and ST 1 VT RSTV is a parallelogram Given: Prove: R V T.

Q: Find the dot product of the following vectors →uu→ and →vv→.. Refer to image below →uu→ ⋅⋅…

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Q: Find the cross product x . Is the resulting vector perpendicular to the given vectors? O ; yes O ;…

A: Vectors < -1, -3, -8 > and < 7, 4, -5> . To find cross product.

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: Let v1 = and vz =. Answer the following: (a) Give three vectors in span{V1,V2}. (b) Is w = contained…

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Q: Compute the length of the following vector: V 5 1 2

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Q: If p = 2i +j - kand q  = i - 3j +2kdetermine the norm of the addition of p and q, and the magnitude.

A: Consider the given information. p=2i+j-kq=i-3j+2k Find the sum of p and q. p+q=2i+j-k+i-3j+2k=3i-j+k

Q: Find the cross product a x b. a4j-9k, -9i+5j + 12k b-i + 3j+k Verify that it is orthogonal to both a…

A: The given vectors  and .The objective is to find the cross product  and verify that is orthogonal…

Q: gj Let v= 2; tj V = 2; +j and w=i+2j. Sketch 20, and

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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: Determine m such that the two vectors are orthogonal.

A: Given : 4mi+j and 9m-25j

Q: Determine the dot product uv, if |||| = 9 and |||| = the angle between the two ㅠ vectors is = 3…

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Q: Q1: If , r₂ and r₂ are three parallel vectors of the same magnitude Prove that ₁+₂+3 is equally…

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Q: Lets vectors V and U be such that |v|=3 and |u|= 4. the angle between v and u is 30 degrees. find…

A: Given: u→=4    and   v→=3 Angle between vectors u and v is: 30°

Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: Consider the two vectors u = 5i+j-4k and v=3i+j - 4k Find the cross product u x v. U XV= j+ k

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Q: Q1.A. For the figure shown below, at what condition the vectors X and Y are orthogonal B -B 1 1

A: Vectors

Q: Find the Euclidean norm of the given vector. Hint: 7 = 49, 24? = 576 V = 24 ||v|| = Ex: 1

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Q: What is the volume, in cubic ft, of a cylinder with a height of 15ft and a base radius of 1oft, to…

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Q: Given v = -8i - 4j and w = -6i + 4j  b. Find vectors v1 and v2 such that v1 is parallel to w,v2 is…

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Q: Check whether u = 6i – 2j+k and v=-4i – 3j+9k parallel or not are

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Q: Vectors. v=i-2j+k, w= i +2j-3K a) Compute the length of V-W.

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Q: Find the cross product (i+e¹j+e¯¹k) × (5i + etj − e−k).

A: Step 1:Here need cross product of ,(i+etj+e−tk)×(5i+etj−e−tk) If a=ai+bj+ck and b=xi+yj+zk given…