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

Let $$\vec{v}=2 \hat{i}+2 \hat{j}-\hat{k}$$ and $$\bar{w}=\hat{i}+3 \hat{k}$$. If $$\bar{u}$$ is a unit vector, then the maximum value of the scalar triple product $$[\bar{u} \bar{v} \bar{w}]$$ is

A
$$\sqrt{6}$$
B
$$\sqrt{10}$$
C
$$\sqrt{13}$$
D
$$\sqrt{89}$$
2
MHT CET 2021 23th September Morning Shift
+2
-0

If $$\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{c}}=3 \hat{\mathrm{i}}+\hat{\mathrm{j}}$$ and $$\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}}$$ is perpendicular to $$\overline{\mathrm{c}}$$, then $$\lambda=$$

A
5
B
2
C
3
D
4
3
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
$$\frac{5}{3} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$$
4
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
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