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…

A:

Q: Given u = 4i - 7j and v=-6i+ 9j, what is u - v?

A:

Q: : For given vectors, a-2i - j+ 2k and b=-i + j- k, find the unit vector in the direction the vector…

A:

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 =

A:

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: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

A:

Q: Let a = (5, — 4) and ☎ = ( − 4, k). - - Find k so that a and will be orthogonal (form a 90 degree…

A: Given thatCondition of vectors orthogonality. Two vectors a and b are orthogonal, if their dot…

Q: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

A: If v = 7i + 3j and w = 4i - 5j, find the vector v - w

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

A:

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

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