Let a = i - k , b =x i + j +(1-x) k and c =y i +x j +(1+x-y) k . Then [ array lll a & ~b…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
Let \(\vec{a}=\hat{i}-\hat{k}, \vec{b}=x \hat{i}+\hat{j}+(1-x) \hat{k}\) and
\(\overrightarrow{\mathrm{c}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+(1+x-y) \hat{\mathrm{k}} .\) Then \(\left[\begin{array}{lll} \overrightarrow{\mathrm{a}} & \overrightarrow{\mathrm{~b}} & \overrightarrow{\mathrm{c}} \end{array}\right]\) depends on
\(\overrightarrow{\mathrm{c}}=y \hat{\mathrm{i}}+x \hat{\mathrm{j}}+(1+x-y) \hat{\mathrm{k}} .\) Then \(\left[\begin{array}{lll} \overrightarrow{\mathrm{a}} & \overrightarrow{\mathrm{~b}} & \overrightarrow{\mathrm{c}} \end{array}\right]\) depends on
- only x
- only y
- neither x nor y
- both x and y
Answer
(C) neither x nor y
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