1
MHT CET 2021 23th September Morning Shift
+2
-0

If $$3 \hat{j}, 4 \hat{k}$$ and $$3 \hat{j}+4 \hat{k}$$ are the position vectors of the vertices $$A, B, C$$ respectively of $$\triangle A B C$$, then the position vector of the point in which the bisector of $$\angle \mathrm{A}$$ meets $$\mathrm{BC}$$ is

A
$$\frac{5}{3} \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$$
B
$$5 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$$
C
$$5 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$$
D
$$\frac{5}{3} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$$
2
MHT CET 2021 22th September Evening Shift
+2
-0

If the vectors $$2 \hat{i}-\hat{j}-\hat{k} ; \hat{i}+2 \hat{j}-3 \hat{k}$$ and $$3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ are coplanar, then the value of $$\lambda$$ is

A
$$-$$8
B
$$-$$4
C
$$-$$2
D
$$-$$1
3
MHT CET 2021 22th September Evening Shift
+2
-0

The vector equation of the line whose Cartesian equations are $$y=2$$ and $$4 x-3 z+5=0$$ is

A
$$\overline{\mathrm{r}}=(2 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})+\lambda(4 \hat{\mathrm{i}}-3 \hat{\mathrm{k}})$$
B
$$\bar{r}=\left(2 \hat{j}-\frac{5}{3} \hat{k}\right)+\lambda(3 \hat{i}+4 \hat{k})$$
C
$$\bar{r}=\left(2 \hat{j}-\frac{5}{3} \hat{k}\right)+\lambda(3 \hat{i}-4 \hat{k})$$
D
$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}})$$
4
MHT CET 2021 22th September Morning Shift
+2
-0

The position vector of the point of inersection of the medians of a triangle, whose vertices are $$A(1,2,3), B(1,0,3)$$ and $$C(4,1,-3)$$ is

A
$$6 \hat{i}+3 \hat{j}+3 \hat{k}$$
B
$$2 \hat{i}+\hat{j}+\hat{k}$$
C
$$3 \hat{i}+\hat{j}+\hat{k}$$
D
$$\hat{i}+\hat{j}+\hat{k}$$
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