Question

Prove that the following vectors are coplanar.
(a) i-2j+3k, -21 +3j - 4k, i -3j+5k with solutions
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Answer 1

Proved, Vectors are Coplanar

Step-by-step explanation:

Three vectors $a^\rightarrow,b^\rightarrow$ and $c^\rightarrow$ are coplanar if

$[a^\rightarrow,b^\rightarrow,c^\rightarrow]=0$

given=

$a^\rightarrow=i-2j+3k\\b^\rightarrow=-2i+3j-4k\\c^\rightarrow=i-3k+5k$

$[a^\rightarrow b^\rightarrow c^\rightarrow ]=\begin{vmatrix} i&j & k\\ 1&-2 & 3\\ -2& 3 & -4\\ 1& -3& 5\end{vmatrix}$

$\Rightarrow1(15-(12)]-(-2)[-10-(-4)+3(6-3)\\\Rightarrow1(3)+2(-6)+9\\\Rightarrow3-12+9\\\Rightarrow12-12=0$