Position vectors of two points are p(2i + j + 3k)

Question

Position vectors of two points are \(P(2\hat{i} + \hat{j} + 3\hat{k}) \) and \(Q(-4\hat{i} - 2\hat{j } + \hat{k}).\) Equation of plane passing through Q and perpendicular of PQ is

(a) \(\vec{r}.(6\hat{i} + 3\hat{j} + 2\hat{k}) = 28\)

(b) \(\vec{r}.(6\hat{i} + 3\hat{j} + 2\hat{k}) = 32\)

(c) \(\vec{r}.(6\hat{i} + 3\hat{j} + 2\hat{k}) + 28 = 0 \)

(d) \(\vec{r}.(6\hat{i} + 3\hat{j} + 2\hat{k}) + 32 = 0\)

Answer 1

Answer is (c)

Let position vector of point P.

and position vector of point Q.

then \(\vec{PQ}\)  position vector of Q- position of vector of P

∴ Equation of plane passing through point Q(\(\vec{b}\)) perpendicular to PQ is