The point collinear with $(1,-2,-3)$ and $(2,0,0)$ among the following is

Question

Aicharya · Accepted Answer

Let $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}+0 \hat{\mathbf{j}}+0 \hat{\mathbf{k}}$ Now take option (c). Let $\mathbf{c}=0 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ Now, a $\begin{aligned} & \mathbf{a} \cdot(\mathbf{b} 	imes \mathbf{c})=\left|\begin{array}{ccc} 1 & -2 & -3 \ 2 & 0 & 0 \ 0 & -4 & -6 \end{array}ight| \ & =1(0)+2(-12)-3(-8)=-24+24=0 \end{aligned}$ $\because$ Option (c) is correct.

The point collinear with $(1,-2,-3)$ and $(2,0,0)$ among the following is

Solution