Let u = 3ai +j+ 4ak and v = 3i + (a+3)j – 4k. (a) Find the values of a if u and v are orthogonal. (b) If a = 2, find the angle between u and v.

Q: Use the dot product to determine whether v = 5i and w = -6j are orthogonal.

A: Given:

Q: Find the cross product a × b. a = j + 9k,    b = 4i − j + 2k       Verify that it is orthogonal…

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Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

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Q: Q2: Find the angle between the vectors à and b where a = i+ 2j – k and b = -i+j-2k.

A: The angle between two vectors A→ and B→ is calculated as, cosθ=A→.B→AB The given vectors are,…

Q: Let a = ci +jand b 7i + 56j. Find c so that a and b are orthogonal. %3D %D C =

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Q: Use the dot product to determine whether v = 5i and w = -6i are orthogonal.

A: The given vector is v=5i  and  w=6i known fact: Two vectors a and b are orthogonal (perpendicular)…

Q: Find the angle between a and b where -6a+2b=2i+j-8k and 2a-b=3i-4j+k

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Q: Let v = (5,1,-2) and w =(4,-4,3). Calculate v w.

A: Given,v=5i+j-2kw=4i-4j+3kWe know that if (a1i+b1j+c1k).(…

Q: 2. Find the directions cosines of AB. a. Ā = (-1,2,3) and B = (4, –3, 1) %3D

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Q: Given u = - i+j, v = 10i-4j, and w= -8j, find proju (v + w).

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Q: Use the dot product to determine whether v = 2i + 8j and w = 4i - j are orthogonal.

A: Given: v=2i+8jw=4i-j