1
MHT CET 2021 22th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are mutually perpendicular vectors having magnitudes $$1,2,3$$ respectively, then $$\left[\begin{array}{lll}\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}} & \overline{\mathrm{b}}-\overline{\mathrm{a}} & \overline{\mathrm{c}}\end{array}\right]=$$

A
12
B
18
C
0
D
6
2
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$$-$$2
B
4
C
$$-$$4
D
2
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $${\pi \over 2} < \theta < \pi$$ and $$|\overline a | = 5,|\overline b | = 13,|\overline a \times \overline b | = 25$$, then the value of $$\overline a \,.\,\overline b$$ is

A
$$-$$12
B
60
C
$$-$$60
D
$$-$$13
4
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$|\bar{a} \times \bar{b}|^2+(\bar{a} \cdot \bar{b})^2=144$$ and $$|\bar{a}|=4$$, then $$|\bar{b}|=$$

A
8
B
12
C
3
D
16
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