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1) 2) Use the vectors u = 2i - j, v = 21 - 3j, and w = -3i + 5j to evaluate the expression. 2v - u + w Find a unit vector in the same direction as the given vector. a = 201 - 21j
2. Which of the following pairs of vectors are orthogonal? (a) v = 3i - 2j, w = --i +2j (b) v = -2i, w = 5j (c) v = -i + 2j, w = -1 (d) v = 2i – 3j, w = -2i + 3j (e) None of these
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]
Suppose u^bar = -4i - 3j - 5k, v^bar = -2i - 3j - 2k and w^bar = i + 3j + 5k. Compute the following values: |u^bar| + |v^bar| = _______ |-6u^bar| + 5|v^bar| = _______ |8u^bar - 5v^bar + w^bar| = _______ 1/|w^bar| w^bar = _______ |1/|w^bar| w^bar| = _______ Enter vector lengths/magnitudes as numbers. Enter vectors using i, j, k notation. For example, 3i + 4j - 2k Use exact values or at least 4 decimal place...
Let A? =2i+3j and B? =4i?2j. Plot vectors A and B. Draw the vectors with their tails at the origin.
if v=-4i+2j and w=2i-3j then find a= v+w b=b-w c=3v d=2v+2w 7. If v =-4i+ 2j and w = 2i - 3j. Then find (Section 7.6) a. vw b. v -w C. 3v d. 2v2w
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a) 30 - 5V._b) 2V - W'. 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculato
1- Two vectors are given as u = 2 – 5j and v=-{+3j. a- Find the vector 2u +3v (by calculation, not by drawing). (4 pts) b- Find the magnitudes luand il of the two vectors. (4 pts) c- Calculate the scalar product u•v. (5 pts) d- Find the angle between the vectors u and v. (6 pts) - Calculate the vector product uxv. (6 pts)
vector u= 2i-j vector v= -2i+3J-3K find the component vector u perpendicular to v
For a = 2i - 3j + 4k, b = 5i + 2j + 6k, find a times b For a = -5i + 3j - 6k, b = 2i - 2j + 3k, find a times b For a = 7i - j + 3k, b = i + 3j - 4k, find a times b For a = 2i + 3j + 5k, b = 4i + 2j - 3k, find a times b