MHT CET 2023 11th May Morning Shift | Vector Algebra Question 127 | Mathematics

If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \overline{\mathrm{b}}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

$$\left(\frac{\pi}{4}\right)$$

$$\left(\frac{\pi}{3}\right)$$

$$\cos ^{-1}\left(\frac{1}{3}\right)$$

$$\cos ^{-1}\left(\frac{2}{7}\right)$$

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$(\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}$$ and $$\bar{a} \cdot \bar{b}=3$$, then the value of $$\bar{a} \times(\bar{b} \times \bar{c})$$ is

$$3 \bar{b}-4 \bar{c}$$

$$4 \overline{\mathrm{a}}-3 \overline{\mathrm{b}}$$

$$4 \bar{b}-3 \bar{c}$$

$$3 \overline{\mathrm{a}}-4 \overline{\mathrm{c}}$$

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$\bar{p}=\hat{i}+\hat{j}+\hat{k}$$ and $$\bar{q}=\hat{i}-2 \hat{j}+\hat{k}$$. Then a vector of magnitude $$5 \sqrt{3}$$ units perpendicular to the vector $$\bar{q}$$ and coplanar with $$\bar{p}$$ and $$\bar{q}$$ is

$$5(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$$

$$5(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$$

$$5(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})$$

$$5(\hat{i}+\hat{j}+\hat{k})$$

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $$\bar{a}$$ and $$\bar{b}$$ are two unit vectors such that $$\bar{a}+2 \bar{b}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

$$\frac{\pi}{3}$$

$$\frac{\pi}{6}$$

$$\frac{\pi}{4}$$

$$\frac{2 \pi}{3}$$

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