CUET Mathematics - The unit vector perpendicular to each of the vectors a+b and a-b, where a=i+j+k and b=i+2 j+3 k, is : | PYQs + Solutions

CUET Mathematics

Algebra

Medium

core

$\frac{1}{\sqrt{6}} \hat{i}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{1}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{2}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

✅ Correct Option: 4

Related questions:

3 June Shift 1

Let $\vec{a} = \hat{i} + 4\hat{j} + 2\hat{k}$ , $\vec{b} = 3\hat{i} - 2\hat{j} + 7\hat{k}$ and $\vec{c} = 2\hat{i} + \hat{j} + 4\hat{k}$ . A vector $\vec{d}$ which is perpendicular to both $\vec{a}$ and $\vec{b}$ , and $\vec{c} \cdot \vec{d} = 14$ , is:

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Let $\vec{a} = 2\hat{i} - \hat{j} \vec{b} - 4\hat{j} + k\,\text{and}\,\vec{c} = \hat{i} + 2\hat{k}$ . If $\vec{d}$ is a vector perpendicular to both $\vec{a}$ and $\vec{b}$ such that $\vec{c} \cdot \vec{d} = 34$ , then $|\vec{d}|$ is equal to

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Which of the following statements are true?

(A) If $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ , then $x, y, z$ are called direction ratios of $\vec{r}$ .

(B) For any two vectors $\vec{a}$ and $\vec{b}$ , $\vec{a} + \vec{b} = \vec{b} + \vec{a}$

(D) Projection of $\vec{b}$ on $\vec{a}$ is $\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2}$

Choose the correct answer from the options given below:

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