1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \bar{b}=-\hat{i}+2 \hat{j}-4 \hat{k}$$ and $$\bar{c}=\hat{i}+\hat{j}-2 \hat{k}$$, then $$(\bar{a} \times \bar{b}) \cdot(\bar{a} \times \bar{c})=$$

A
$$-$$30
B
84
C
70
D
984
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$ and $$\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$$. If $$\overline{\mathrm{c}}$$ is a vector such that $$\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$$ and the angle between $$\overline{\mathrm{a}} \times \overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ is $$60^{\circ}$$. Then $$|(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|=$$

A
$$\frac{3 \sqrt{3}}{2}$$
B
$$\frac{3}{2}$$
C
$$3 \sqrt{3}$$
D
$$\frac{\sqrt{3}}{2}$$
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The projection of $$\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$$ on $$\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$$ is

A
5
B
$$5 \sqrt{6}$$
C
$$\frac{5}{\sqrt{6}}$$
D
$$\sqrt{6}$$
4
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}$$ and $$\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ are coplanar, then $$\lambda$$ is the root of the equation

A
$$\mathrm{x}^2+3 \mathrm{x}=6$$
B
$$x^2+2 x=4$$
C
$$x^2+3 x=4$$
D
$$x^2+2 x=6$$
MHT CET Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12