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natulia
7 days ago
9

Let a⃗ =4ı^−2ȷ^, b⃗ =−3ı^+5ȷ^, and e⃗ =2a⃗ +3b⃗ . part a write vector e⃗ in component form.

Mathematics
1 answer:
zzz [4K]7 days ago
4 0

We are provided with the vectors:

Vector \vec{a}=4\hat i-2\hat j and \vec{b}=-3\hat i+5\hat j.

Expressing a vector in component form involves detailing each separate component.

Our vector \vec e can be represented as:

\vec e =2\vec a+3\vec b

Now, considering 2 \vec a=2(4\hat i- 2 \hat j)=8 \hat i -4 \hat j

and 3 \vec b= 3(-3 \hat i +5\hat j)=-9 \hat i + 15\hat j

By substituting the values of 2 \vec a and 3\vec b, we find:

\vec e = 8 \hat i-4 \hat j-9 \hat i + 15 \hat j=- \hat i+11 \hat j

Thus, the component form of vector 'e' is:

\vec e= -\hat i+11\hat j

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