TG EAPCET 2025 (Online) 2nd May Morning Shift | Vector Algebra Question 26 | Mathematics

The point of intersection of the line joining the points $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and the plane passing through the points $\hat{\mathbf{i}}, 2 \hat{\mathbf{j}}, 3 \hat{\mathbf{k}}$ is

$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$

$\frac{1}{7}(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})$

$\hat{\mathbf{i}}-3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$

$\frac{1}{7}(15 \hat{\mathbf{i}}-10 \hat{\mathbf{j}}-9 \hat{\mathbf{k}})$

TG EAPCET 2025 (Online) 2nd May Morning Shift

MCQ (Single Correct Answer)

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If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=12$ and $|\mathbf{a}-\mathbf{b}|=13$, then $|2 \mathbf{a}+\mathbf{b}|=$

$2 \sqrt{61}$

$61 \sqrt{2}$

TG EAPCET 2025 (Online) 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are two vectors, then $(\mathbf{a}+2 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})$

$2 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$

$6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$

$14 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$

$14 \hat{\mathbf{i}}+42 \hat{\mathbf{j}}-35 \hat{\mathbf{k}}$

TG EAPCET 2024 (Online) 11th May Morning Shift

MCQ (Single Correct Answer)

-0

$2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ are the position vectores of two points $A$ and $B$ respectively and $C$ divides $A B$ in the ratio $3: 2$ : If $3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is the position of vector of a point $D$, then the unit vector in the direction of $C D$ is

$\frac{1}{7 \sqrt{2}}(8 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})$

$\frac{1}{\sqrt{266}}(4 \hat{\mathbf{i}}-13 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})$

$\frac{1}{3 \sqrt{42}}(8 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+17 \hat{\mathbf{k}})$

$\frac{1}{7 \sqrt{2}}(8 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$

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