3 months ago

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

1 answer:

zzz [12.3K]3 months 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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