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

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

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    2022-01-04T19:02:26+00:00

    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

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