If \( \left|\begin{array}{lll}(x-a)^{2} & (x-b)^{2} & (x-c)^{2} \\ (y-a)^{2} & (y-b)^{2} & (y-c)...
If \( \left|\begin{array}{lll}(x-a)^{2} & (x-b)^{2} & (x-c)^{2} \\ (y-a)^{2} & (y-b)^{2} & (y-c)^{2} \\ (z-a)^{2} & (z-b)^{2} & (z-c)^{2}\end{array}\right|=0 \) and the vector \( X=\left(x^{2}, x, 1\right), Y=\left(y^{2}, y, 1\right) \) and \( Z=\left(z^{2}, z, 1\right) \) are non coplanar, then the vectors \( \left(a^{2}, a, 1\right),\left(b^{2}, b, 1\right) \) and \( \left(c^{2}, c, 1\right) \) are:
(a) Coplanar
(b) Non coplanar
(c) Collinear
(d) Non collinear
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | Consider the points \( A(\vec{a}) ; B(\vec{b}) ; C(\vec{c}) \) and \( D(\vec{d}) . x \) is the d... |
| 2023-06-09 | Let \( O A B C \) is a tetrahedron with equal edges and \( \overrightarrow{O A}=\vec{a}, \overri... |
| 2023-06-09 | If \( a, b, c \) are the \( \mathrm{p}^{\text {th }}, \mathrm{q}^{\text {th }}, \mathrm{r}^{\tex... |
| 2023-06-09 | If \( \hat{i} \times[(\vec{a}-\hat{j}) \times \hat{i}]+\hat{j} \times[(\vec{a}-\hat{k}) \times \... |
| 2023-06-09 | Let a be a real number and \( \vec{\alpha}=\hat{i}+2 \hat{j}, \vec{\beta}=2 \hat{i}+a \hat{j}+10... |
| 2023-06-09 | Let \( \vec{a}=\lambda \hat{i}+2 \hat{j}+\hat{k}, \hat{b}=\hat{i}+\lambda \hat{j}-\hat{k} \) and... |
| 2023-06-09 | \( (\vec{d}+\vec{a}) \cdot(\vec{a} \times(\vec{b} \times(\vec{c} \times \vec{d}))) \) simplifies... |
| 2023-06-09 | Consider a plane \( \pi: \vec{r} \cdot \vec{n}=d \) (where \( \vec{n} \) is not a unit vector). ... |
| 2023-06-09 | Let \( \vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}, \vec{b}=b_{1} \hat{i}+b_{2} \hat{j}+b_... |
| 2023-06-09 | If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three mutually perpendicular unit vectors and \(... |
| 2023-06-09 | If \( \left|\begin{array}{lll}(x-a)^{2} & (x-b)^{2} & (x-c)^{2} \\ (y-a)^{2} & (y-b)^{2} & (y-c)... |
| 2023-06-09 | The angle \( \theta \) between two non-zero vectors \( a \) and \( b \) satisfies the relation
\... |
| 2023-06-09 | The position vector of a point \( P \) is \( \vec{r}=x \vec{i}+y \vec{j}+z \vec{k} \), where \( ... |
| 2023-06-09 | If \( a \) is real constant and \( A, B, C \) are variable angles and \( \sqrt{a^{2}-4} \tan A... |
| 2023-06-09 | If \( a=x \hat{i}+y \hat{j}+z \hat{k}, b=y \hat{i}+z \hat{j}+x \hat{k} \) and \( c=z \hat{i}+x \... |
| 2023-06-09 | If \( \vec{a}=x \hat{i}+y \hat{j}+z \hat{k}, \vec{b}=y \hat{i}+z \hat{j}+x \hat{k} \) and \( \ve... |
| 2023-06-09 | \( \vec{a}=\hat{i}-\hat{j} ; \vec{b}=\hat{j}-\hat{k}, \vec{c}=\hat{k}-\hat{i} \). If \( \vec{d} ... |
| 2023-06-09 | If \( V_{1}, V_{2}, V_{3} \) are the volumes of parallelopiped, triangular prism and tetrahedron... |
| 2023-06-09 | If \( a=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k}) \) and \( b=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \ha... |
| 2023-06-09 | The value of \( \vec{r} \) if exist where \( \vec{r}=\vec{a}+\lambda \vec{b} \) and \( \vec{r} \... |
| 2023-06-09 | Volume of tetrahedron determined by vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) is \( \frac... |
0