Find the vector projVu.
v=3i−j+3k,
u=10i+11j+2k
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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]
a b с 3. If a = i-2j+3k and b 3i+j + 2k, find a unit vector along c which is a linear combination of a and b and also perpendicular to b.
vector u= 2i-j vector v= -2i+3J-3K find the component vector u perpendicular to v
5. Find the i) scalar and ii) vector projections of v onto u if u = 7i+j – 2k and v= 3i -5j +2k
1. 2. Find u v and the angle between vector u and v for a) u = 2i – 2j + k, v = 3i + 4k b) u = v3i – 7j, v = v3i+j – 2k c) u = 2i +j, v= i + 2j – k
Vector (Cross) Product 1. Find the vector product (2j-2k) x 5k. Sketch all three vectors onto the coordinate system below Answer: 10 Find the vector product of i+4j-3k and -2i+j-5k. Prove that your answer is perpendicular to the first two vectors by using the dot product Answer: -17i+11j+9k or 17i-11j-9k, depending on the order in which you took the cross product. 2.
Find a vector that is orthogonal to u = -2i+ 5j - 3k and w = 3i+2j+k.
Find the angle between u = -91 +3j - 10k and v=3i+ 10j - 2k in radians. Round to two decimal places. ОА. 1.57 Ов. 0.16 ОО с. 1.41 OD. 1.49
a. Find the projection of u 21j+3k on y- -i+3j+2k. Hence resolve u into two vectors, one parallel to y and the other perpendicular to v. b. Resolve v into two vectors, one parallel to υ and the other perpendicular to u.
Let u = -71 - 9j and v = -3i +3j. Find ū+v Select the correct answer below: O 4i – 12 O 4i +12j O 10i+6j 0 -101 - 6j