1
MHT CET 2023 10th May Evening Shift
+2
-0

If $$\bar{p}=\hat{i}+\hat{j}+\hat{k}$$ and $$\bar{q}=\hat{i}-2 \hat{j}+\hat{k}$$. Then a vector of magnitude $$5 \sqrt{3}$$ units perpendicular to the vector $$\bar{q}$$ and coplanar with $$\bar{p}$$ and $$\bar{q}$$ is

A
$$5(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$$
B
$$5(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$$
C
$$5(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})$$
D
$$5(\hat{i}+\hat{j}+\hat{k})$$
2
MHT CET 2023 10th May Evening Shift
+2
-0

If $$\bar{a}$$ and $$\bar{b}$$ are two unit vectors such that $$\bar{a}+2 \bar{b}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

A
$$\frac{\pi}{3}$$
B
$$\frac{\pi}{6}$$
C
$$\frac{\pi}{4}$$
D
$$\frac{2 \pi}{3}$$
3
MHT CET 2023 10th May Evening Shift
+2
-0

If $$\overline{\mathrm{a}}=\mathrm{m} \overline{\mathrm{b}}+\mathrm{nc}$$, where $$\overline{\mathrm{a}}=4 \hat{\mathrm{i}}+13 \hat{\mathrm{j}}-18 \hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overline{\mathrm{c}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$$, then $$\mathrm{m}+\mathrm{n}=$$

A
1
B
2
C
3
D
$$-1$$
4
MHT CET 2023 10th May Evening Shift
+2
-0

If the volume of tetrahedron, whose vertices are with position vectors $$\hat{i}-6 \hat{j}+10 \hat{k},-\hat{i}-3 \hat{j}+7 \hat{k}, 5 \hat{i}-\hat{j}+\lambda \hat{k}$$ and $$7 \hat{i}-4 \hat{j}+7 \hat{k}$$ is 11 cubic units, then value of $$\lambda$$ is

A
4
B
5
C
7
D
6
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