Question

Two vectors are given by A vector=-2i+j-3k and B vector =5i+3j-2k. If 3A vector +2B vector-C vector =0 then third vector is:

Answer 1

Given:

$\vec{A}=-2i+j-3k$

$\vec{B}=5i+3j-2k$

$3\vec{A}+2\vec{B}-\vec{C}=0$

To find:

The third vector, i.e., $\vec{C}$.

Solution:

Let $\vec{C}=ai+bj+ck$.

We have,

$3\vec{A}+2\vec{B}-\vec{C}=0$

$3(-2i+j-3k)+2(5i+3j-2k)-(ai+bj+ck)=0i+0j+0k$

$-6i+3j-9k+10i+6j-4k-ai-bj-ck=0i+0j+0k$

$(-6+10-a)i+(3+6-b)j+(-9-4-c)k=0i+0j+0k$

$(4-a)i+(9-b)j+(-13-c)k=0i+0j+0k$

On comparing both sides, we get

$4-a=0\Rightarrow a=4$

$9-b=0\Rightarrow b=9$

$-13-c=0\Rightarrow c=-13$

Now,

$\vec{C}=ai+bj+ck$

$\vec{C}=4i+9j+(-13)k$

$\vec{C}=4i+9j-13k$

Therefore, the third vector is $\vec{C}=4i+9j-13k$.

Answer 2

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