1
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
$$-1$$
2
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+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
3
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Scalar projection of the line segment joining the points $$\mathrm{A}(-2,0,3), \mathrm{B}(1,4,2)$$ on the line whose direction ratios are $$6,-2,3$$ is

A
$$\frac{23}{7}$$
B
1
C
7
D
$$\frac{1}{7}$$
4
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$$ and $$\overline{\mathrm{c}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}$$ are such that $$(\bar{a}+\lambda \bar{b})$$ is perpendicular to $$\bar{c}$$, then the value of $$\lambda$$ is

A
$$\frac{5}{11}$$
B
$$\frac{11}{5}$$
C
$$\frac{-11}{5}$$
D
$$\frac{-5}{11}$$
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