1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The volume of parallelopiped, whose coterminous edges are given by $$\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \vec{v}=\hat{i}+\hat{j}+3 \hat{k}, \bar{w}=2 \hat{i}+\hat{j}+\hat{k}$$ is 1 cu. units. If $$\theta$$ is the angle between $$\bar{u}$$ and $$\bar{w}$$, then the value of $$\cos \theta$$ is

A
$$\frac{3}{4}$$
B
$$\frac{5}{6}$$
C
$$\frac{1}{5}$$
D
$$\frac{1}{6}$$
2
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\bar{a}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}, \bar{b}=x \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+(1-x) \hat{\boldsymbol{k}}$$ and $$\bar{c}=y \hat{\boldsymbol{i}}+x \hat{\boldsymbol{j}}+(1+x-y) \hat{\boldsymbol{k}}$$, then $$[\bar{a} \bar{b} \bar{c}]$$ depends on

A
only $$y$$
B
neither $$x$$ nor $$y$$
C
both $$x$$ and $$y$$
D
only $$x$$
3
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\bar{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\bar{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ be two vectors. If $$\bar{c}$$ is a vector such that $$\bar{b} \times \bar{c}=\bar{b} \times \bar{a}$$ and $$\bar{c} \cdot \bar{a}=0$$, then $$\bar{c} \cdot \bar{b}$$ is equal to

A
$$-\frac{1}{2}$$
B
$$\frac{3}{2}$$
C
$$\frac{1}{2}$$
D
$$-\frac{3}{2}$$
4
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

The magnitude of the projection of the vector $$2 \hat{\mathbf{i}}+ 3\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ on the vector perpendicular to the plane containing the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ is

A
$$3 \sqrt{6}$$ units
B
$$\frac{\sqrt{3}}{2}$$ units
C
$$\frac{1}{\sqrt{6}}$$ units
D
$$\sqrt{\frac{3}{2}}$$ units
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12
© ExamGOAL 2024