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Show that the four points and with position vectors , , and respectively, are coplanar.
Show that the four points $A, B, C$ and $D$ with position vectors $4\hat{\imath} + 5\hat{\jmath} + \hat{k}$, $-\hat{\jmath} - \hat{k}$, $3\hat{\imath} + 9\hat{\jmath} + 4\hat{k}$ and $4(-\hat{\imath} + \hat{\jmath} + \hat{k})$ respectively, are coplanar.
Given: Four points $A, B, C, D$ with position vectors $4\hat{\imath} + 5\hat{\jmath} + \hat{k}$, $-\hat{\jmath} - \hat{k}$, $3\hat{\imath} + 9\hat{\jmath} + 4\hat{k}$ and $4(-\hat{\imath} + \hat{\jmath} + \hat{k})$
To show: Points $A, B, C, D$ are coplanar
Answer
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From ISC 2018 Mathematics Paper 1, question 16(b).