If x is parallel to y and z where x = 2i + j | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $x$ is parallel to both $y$ and $z$,it implies that $x$,$y$,and $z$ are coplanar. For three vectors to be coplanar,their scalar triple

Vedclass · Accepted Answer

$ \pm \sqrt{7} $

Vedclass · Answer

(C) Given that $x$ is parallel to both $y$ and $z$,it implies that $x$,$y$,and $z$ are coplanar. For three vectors to be coplanar,their scalar triple product must be zero,i.e.,$[x, y, z] = 0$. This is represented by the determinant: $\begin{vmatrix} 2 & 1 & \alpha \ \alpha & 0 & 1 \ 5 & -1 & 0 \end{vmatrix} = 0$ Expanding the determinant along the first row: $2(0(0) - 1(-1)) - 1(\alpha(0) - 1(5)) + \alpha(\alpha(-1) - 0(5)) = 0$ $2(1) - 1(-5) + \alpha(-\alpha) = 0$ $2 + 5 - \alpha^2 = 0$ $7 - \alpha^2 = 0$ $\alpha^2 = 7$ $\alpha = \pm \sqrt{7}$ Thus,the correct option is $C$.

If $x$ is parallel to $y$ and $z$ where $x = 2i + j + \alpha k$,$y = \alpha i + k$ and $z = 5i - j$,then $\alpha$ is equal to

Similar Questions

If the vectors $2i - j + k$,$i + 2j - 3k$,and $3i + \lambda j + 5k$ are coplanar,then $\lambda = $

Let $\vec{a} = \hat{i} + 2\hat{j} + 4\hat{k}$,$\vec{b} = \hat{i} + \lambda\hat{j} + 4\hat{k}$,and $\vec{c} = 2\hat{i} + 4\hat{j} + (\lambda^2 - 1)\hat{k}$ be coplanar vectors. Then the non-zero vector $\vec{a} \times \vec{c}$ is:

If the vectors $i+3j-2k$,$2i-j+4k$ and $3i+2j+xk$ are coplanar,then the value of $x$ is:

For three vectors $a, b, c$,the value of $[a \times b, b \times c, c \times a]$ is equal to:

The volume of a tetrahedron whose vertices are $4 \hat{i}+5 \hat{j}+\hat{k}$,$-\hat{j}+\hat{k}$,$3 \hat{i}+9 \hat{j}+4 \hat{k}$ and $-2 \hat{i}+4 \hat{j}+4 \hat{k}$ is (in cubic units)

Vedclass Test Series

Exam Paper Generator

Online Exam Module