Question

Express the vector 5u + 2w in the form v = 1i + 2j + 3k if u = [ 5, - 4. 2] and w =[ -4, 3, 5].

Answer 1

Answer:
`\vec{v}=1(17)\hat{i}+2(7)\hat{j}+3(6.67)\hat{k}`

Explanation:

Since we have given that

`\vec{u}=5\hat{i}-4\hat{j}+2\hat{k}\\\\and\\\\\vec{w}=}`

We need to find the value of

`5\vec{u}+2\vec{w}` in the form of
`\vec{v}=1\hat{i}+2\hat{j}+3\hat{k}`

so, it becomes,

`5(5\hat{i}-4\hat{j}+2\hat{k})+2(-4\hat{i}+3\hat{j}+5\hat{k})\\\\=25\hat{i}-20\hat{j}+10\hat{k}-8\hat{i}+6\hat{j}+10\hat{k}\\\\=17\hat{i}-14\hat{j}+20\hat{k}`

So, in the form of
`\vec{v}`

So, it becomes,

`\vec{v}=1(17)\hat{i}+2(7)\hat{j}+3(6.67)\hat{k}`