Find the vectors whose lengths and directions are given. Try to do the calculati

Question

Find the vectors whose lengths and directions are given. Try to do the calculations without writing. a. The vector with length 5 and direction i is (Type exact answers. using radicals as needed.) b. The vector with length root 2 and direction ? j is (Type exact answers, using radicals as needed) c. The vector with length 1/2 and direction -4/5 j -3/5 k is (Type exact answers, using radicals as needed.) d. The vector with length 7 and direction 6/7 I -2/7 j +3/7 k is (Type exact answers, using radicals as needed)

Explanation / Answer

all the direction vectors given are unit vectors, because all of them have magnitude 1

a) 5(i) = 5i +0j +0k

b) 2(-j) = 0i -2j +0k

c) (1/2)(4/5 j - 3/5 k) = 4/10 j -3/10 k = 0i +4/10 j -3/10 k

d) 7(6/7 i -2/7 j +3/7 k) = 6i -2j +3k

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