The plane \overrightarrow{r}=s(\hat{i}+2 \hat{j}-4 k)+ t(3 i +4 \hat{j}-4 k)+(1-t)(2 \hat{i}-7 \hat{j}-3 \hat{k}) is parallel to the line

Correct Answer is : →r=(−∧i+∧j−∧k)+t(−∧i−2∧j+4∧k)

\overrightarrow{r}=(-\hat{i}+\hat{j}-{ { k^{∧} }})+t(-\hat{i}-2 \hat{j}+4 \hat{k})

\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(\hat{i}-2 \hat{j}+4 \hat{k})

\overrightarrow{r}=(\hat{i}+\hat{j}-\hat{k})+t(-\hat{i}-4 \hat{j}+7 \hat{k})

\overrightarrow{r}=(-\hat{i}+\hat{j}-\hat{k})+t(-2 \hat{i}+2 \hat{j}+4 \hat{k})

\overrightarrow{r}=(-\hat{i}+\hat{j}-3 k)+t(2 \hat{i}+6 \hat{j}-8 \hat{k})

KEAM 2010 Math Paper

Question : 15 of 120

Marks: +1, -0

The plane

→

=s(

∧

−4k)+t(3i+4

∧

−4k)+(1−t)(2

∧

−7

∧

−3

∧

)

is parallel to the line

→
r
=(−
∧
i
+
∧
j
−
∧
k
)+t(−
∧
i
−2
∧
j
+4
∧
k
)
→
r
=(−
∧
i
+
∧
j
−
∧
k
)+t(
∧
i
−2
∧
j
+4
∧
k
)
→
r
=(
∧
i
+
∧
j
−
∧
k
)+t(−
∧
i
−4
∧
j
+7
∧
k
)
→
r
=(−
∧
i
+
∧
j
−
∧
k
)+t(−2
∧
i
+2
∧
j
+4
∧
k
)
→
r
=(−
∧
i
+
∧
j
−3k)+t(2
∧
i
+6
∧
j
−8
∧
k
)

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