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

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FelisFelis FelisFelis · Answer 1 · 2018-10-03T09:29:16+02:00

We have been given that:

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

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

Now, our vector [tex]\vec e[/tex] is given by

[tex]\vec e =2\vec a+3\vec b[/tex]

Now, [tex]2 \vec a=2(4\hat i- 2 \hat j)=8 \hat i -4 \hat j[/tex]

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

Plugging the values of [tex]2 \vec a[/tex] and [tex]3\vec b[/tex], we get:

[tex]\vec e = 8 \hat i-4 \hat j-9 \hat i + 15 \hat j=- \hat i+11 \hat j[/tex]

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

[tex]\vec e= -\hat i+11\hat j[/tex]

ap8997154 ap8997154 · Answer 2 · 2022-02-19T14:37:37+01:00

Vector is an element of a vector space. The value of vector e is -i+11j.

A vector is an element of a vector space.

Given to us

[tex]\vec a = 4i - 2j[/tex]

[tex]\vec b = 3i + 5j[/tex]

[tex]\vec e = 2a + 3b[/tex]

As given to us that e=2a+3b, substitute the value of a and b, we will get,

[tex]\vec e = 2a + 3b\\\\\vec e = 2(4i - 2j) + 3(-3i + 5j)\\\\\vec e = 8i - 4j - 9i + 15j\\\\\vec e = -i +11 j[/tex]

Hence, the value of vector e is -i+11j.

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