1
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ are the position vectores of two points $A$ and $B$ respectively and $C$ divides $A B$ in the ratio $3: 2$ : If $3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is the position of vector of a point $D$, then the unit vector in the direction of $C D$ is
A
$\frac{1}{7 \sqrt{2}}(8 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})$
B
$\frac{1}{\sqrt{266}}(4 \hat{\mathbf{i}}-13 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})$
C
$\frac{1}{3 \sqrt{42}}(8 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+17 \hat{\mathbf{k}})$
D
$\frac{1}{7 \sqrt{2}}(8 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$
2
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A unit vector $\hat{\mathbf{e}}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is coplanar with the vectors $\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$, and $3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-5 \hat{\mathbf{k}}$. If $\hat{\mathbf{e}}$ is perpendicular to the vector $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$, then $2 a^{2}+3 b^{2}+4 c^{2}=$
A
1
B
3
C
-1
D
$\sqrt{2}$
3
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \hat{\mathbf{b}}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{c}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ are three vectors. If $\hat{\mathbf{d}}$ is a normal to the plane of $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ and d. $\hat{\mathbf{c}}=2$, then $|\hat{\mathbf{d}}|=$
A
$\sqrt{6}$
B
$2 \sqrt{3}$
C
$\sqrt{3}$
D
2
4
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{c}=-\hat{\mathbf{k}}$ are position vectors of two points and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}, \mathbf{d}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are two vectors, then the lines $\mathbf{r}=\mathbf{a}+t \mathbf{b}, \mathbf{r}=\mathbf{c}+s \mathbf{d}$ are
A
skew lines, when $\lambda=\frac{19}{3}$
B
coplanar, $\forall \lambda \in R$
C
skew lines when $\lambda \neq \frac{19}{3}$
D
coplanar, when $\lambda \neq \frac{19}{3}$
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