Given that vectors p and q are perpendicular, where p≠0 and q≠0 show that |2p+3q|²= 4|p|²+9|q|²

Q: The vectors a and b are such so that a = √10, b = 10 Find the value of lax bl. and a b = 30

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Q: ||ī|| = Find the length of the vector = 2 -2 Enter `sqrt(a)' for √Va

A: In this question we will find the Length of the vector.

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: -31 - -4 5 Given the vectors vi = 2 v₂ = 2 and √3 = -4 determine 4 - 2 " Why would you not do the…

A: To determine the value of v1​​×v2​​⋅v3​​, we need to follow the steps for the vector cross product…

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: Q2: write down a unit vector in XY plan making angle of 30° with the positive direction of x-axis?

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Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: 6) Vectors p=3i+j+4k and q=2-1 Determine pxq.qxp and p.q.

A: I have explained everything with in the solution, please go through that.

Q: The vectors į+j and i-į are perpendicular. True False

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Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

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Q: Given the vectors v = 4i + 2j – 3k and w = 3i – 4j + k. Find | 2v- w| А. V41 В. /126 С. V65 D. V138

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Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

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Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

Q: given the followinf vectors, find |u+w| u= -3i+6j w=-2i-5j a- sqrt26 b- sqrt24 c-  -sqrt24 d- 5

A: The vectors u=-3i+6j and w=-2i-5j. Then we have to find u+w.

Q: i+ 2j+ k and w = 2i - j+ 4k. Find the area of the parallelogram with sides given as v and w. !!

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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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