1
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$(\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}$$ and $$\bar{a} \cdot \bar{b}=3$$, then the value of $$\bar{a} \times(\bar{b} \times \bar{c})$$ is

A
$$3 \bar{b}-4 \bar{c}$$
B
$$4 \overline{\mathrm{a}}-3 \overline{\mathrm{b}}$$
C
$$4 \bar{b}-3 \bar{c}$$
D
$$3 \overline{\mathrm{a}}-4 \overline{\mathrm{c}}$$
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+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
$$5(\hat{i}+\hat{j}+\hat{k})$$
3
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+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
$$\frac{2 \pi}{3}$$
4
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+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
$$-1$$
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