MHT CET 2021 22th September Evening Shift | Vector Algebra Question 173 | Mathematics

If the vectors $$2 \hat{i}-\hat{j}-\hat{k} ; \hat{i}+2 \hat{j}-3 \hat{k}$$ and $$3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ are coplanar, then the value of $$\lambda$$ is

$$-$$8

$$-$$4

$$-$$2

$$-$$1

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

The vector equation of the line whose Cartesian equations are $$y=2$$ and $$4 x-3 z+5=0$$ is

$$\overline{\mathrm{r}}=(2 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})+\lambda(4 \hat{\mathrm{i}}-3 \hat{\mathrm{k}})$$

$$\bar{r}=\left(2 \hat{j}-\frac{5}{3} \hat{k}\right)+\lambda(3 \hat{i}+4 \hat{k})$$

$$\bar{r}=\left(2 \hat{j}-\frac{5}{3} \hat{k}\right)+\lambda(3 \hat{i}-4 \hat{k})$$

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}})$$

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

The position vector of the point of inersection of the medians of a triangle, whose vertices are $$A(1,2,3), B(1,0,3)$$ and $$C(4,1,-3)$$ is

$$6 \hat{i}+3 \hat{j}+3 \hat{k}$$

$$2 \hat{i}+\hat{j}+\hat{k}$$

$$3 \hat{i}+\hat{j}+\hat{k}$$

$$\hat{i}+\hat{j}+\hat{k}$$

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

The area of the parallelogram whose diagonals are represented by the vectors $$\bar{a}=3 \hat{i}-\hat{j}-2 \hat{k}$$ and $$\bar{b}=-\hat{i}+3 \hat{j}-3 \hat{k}$$ is

$$\sqrt{266}$$ sq. units

$$\frac{1}{2} \sqrt{266}$$ sq. units

266 sq. units

122 sq. units

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