1
MHT CET 2023 9th May Morning Shift
+2
-0

The distance of the point having position vector $$\hat{i}-2 \hat{j}-6 \hat{k}$$, from the straight line passing through the point $$(2,-3,-4)$$ and parallel to the vector $$6 \hat{i}+3 \hat{j}-4 \hat{k}$$ is units.

A
$$\sqrt{\frac{340}{61}}$$
B
$$\frac{341}{61}$$
C
$$\frac{\sqrt{341}}{61}$$
D
$$\sqrt{\frac{341}{61}}$$
2
MHT CET 2023 9th May Morning Shift
+2
-0

The scalar product of the vector $$\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$$ with a unit vector along the sum of the vectors $$2 \hat{i}+4 \hat{j}-5 \hat{k}$$ and $$\lambda \hat{i}+2 \hat{j}+3 \hat{k}$$ is equal to 1 , then value of $$\lambda$$ is

A
1
B
2
C
3
D
4
3
MHT CET 2023 9th May Morning Shift
+2
-0

If $$[(\bar{a}+2 \bar{b}+3 \bar{c}) \times(\bar{b}+2 \bar{c}+3 \bar{a})] \cdot(\bar{c}+2 \bar{a}+3 \bar{b})=54$$ then the value of $$\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$$ is

A
0
B
1
C
3
D
2
4
MHT CET 2023 9th May Morning Shift
+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
$$\frac{1}{6}$$
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Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
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Inorganic Chemistry
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