Question

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

Answer 1

We have been given that:

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

Component form of a vector implies to write the vector with each individual components.

Now, our vector
`\vec e` is given by

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

Now,
`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`

Plugging the values of
`2 \vec a` and
`3\vec b`, we get:

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

So, the vector 'e' in its component form is given as:

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