BITSAT 2025 | Vector Algebra Question 1 | Mathematics

If $\mathbf{a , b , c}$ are vectors such that $|\mathbf{b}|=|\mathbf{c}|$ then $\{(\mathbf{a}+\mathbf{b}) \times(\mathbf{a}+\mathbf{c})\} \times(\mathbf{b} \times \mathbf{c}) \cdot(\mathbf{b}+\mathbf{c})$ is equal to

BITSAT 2024

MCQ (Single Correct Answer)

-1

Let $ \mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{k}}, \mathbf{b}=x \hat{\mathbf{i}}+\hat{\mathbf{j}}+(1-x) \hat{\mathbf{k}} $ and $ \mathbf{c}=y \hat{\mathbf{i}}+x \hat{\mathbf{j}}+(1+x-y) \hat{\mathbf{k}} $. Then, $ [\mathbf{a} \mathbf{b} \mathbf{c}] $ depends on

only $ y $

only $ x $

both $ x $ and $ y $

neither $ x $ nor $ y $

BITSAT 2024

MCQ (Single Correct Answer)

-1

The magnitude of projection of line joining ( 3,4 , $ 5) $ and $ (4,6,3) $ on the line joining $ (-1,2,4) $ and $ (1,0,5) $ is

$ \frac{4}{3} $

$ \frac{2}{3} $

$ \frac{8}{3} $

$ \frac{1}{3} $

BITSAT 2023

MCQ (Single Correct Answer)

-1

Let $$\mathbf{a}=2 \mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}$$ and $$a$$ unit vector $$\mathbf{c}$$ be coplanar. If $$\mathbf{c}$$ is perpendicular to $$\mathbf{a}$$, then c equals to

$$\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}})$$

$$\frac{1}{\sqrt{2}}(-\hat{\mathbf{j}}+\hat{\mathbf{k}})$$

$$\frac{1}{\sqrt{3}}(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})$$

$$\frac{1}{\sqrt{3}}(-\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})$$

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