Angle between two vector u and v, = cos-1 ()
Using the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A = 6i - 7j and B = 8i - 5j [17.33] (b) A = 3i + 3j and B = 3i - 4j + 2k (c) A = i - 2j + 2k and B = 3j + 4k
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal to a and b. _ [3 marks] (b) Show that the vector from (a) is orthogonal to a and b. [1 mark]
4. [-12 Points) DETAILS SCALCET8 12.3.011. If u is a unit vector, find u v and u. w. (Assume v and w are also unit vectors.) u u v = Uw= 5. [-12 Points] DETAILS SCALCET8 12.3.015. Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = (7,2), b = (3,-1) exact approximate 6. [-/2 points) DETAILS SCALCET8 12.3.019. Find the angle between the vectors. (First find an exact expression...
5. Find the i) scalar and ii) vector projections of v onto u if u = 7i+j – 2k and v= 3i -5j +2k
Find a vector that is orthogonal to u = -2i+ 5j - 3k and w = 3i+2j+k.
2. Given the vectors u = 2i + 3j and v = -3i - 2j (a) (4 points) Plot and label each vector (b) (4 points) Find w = u + v (c) (4 points) Find the unit vector of w
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j - kand C i + 2j - 2k, find: ax (b x c) (ax b) x t i. ii 4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j -...
u=2i-j+k v = 37 - 4k w = -51 +7 QUESTION 1)Find the volume of the parallel face determined by the vectors QUESTION 2) f(x, y, z) = xy + y2 + zx a) Find the gradient vector of function f b) Calculate the gradient vector at point P (1, -1, 2) of function f. c) Direction in the direction of the vector v = 3i + 6j - 2k at point P (1,-1,2) of the function f find the...
Find the vector projVu. v=3i−j+3k, u=10i+11j+2k
Find the angle θ between the vectors in radians and in degrees. u = 5i + 2j + k v = 2i - 5j (a) radians (b) degrees