The equation of the line passing through (-2, 3, 4) and parallel to the vector 2i - j + k is: Option 1: r = (i + j + k) + (2i - j + k) Option 2: r = (2i - j + k) + (i + j + k) Option 3: r = (-2i + 3j + 4k) + (2i - j + k) Option 4: r = (2i - j + k) + (-2i + 3j + 4k)

The answer is 'r = (-2i + 3j + 4k) + (2i - j + k)'. View full solution:

The equation of the line passing through (-2, 3, 4) and paral<=l to the vector 2i - j + k is:

r = (-2i + 3j + 4k) + (2i - j + k)

r = (2i - j + k) + (-2i + 3j + 4k)

CUET Mathematics 2022 4 Aug Shift 1

Algebra

Easy

$\vec{r} = (\hat{i} + \hat{j} + \hat{k}) + \lambda(2\hat{i} - \hat{j} + \hat{k})$

$\vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})$

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

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

✅ Correct Option: 3

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The angle between the vectors $\hat{i} - \hat{j}$ and $\hat{j} - \hat{k}$ is:

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The projection of the vector $2\hat{i} - \hat{j} + 3\hat{k}$ on the vector $3\hat{i} + 2\hat{j} + 6\hat{k}$ is

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Match List - I with List - II.

	List - I (Two given vector)		List - II (Projection of $\vec{a}$ on $\vec{b}$ )
(A)	$\vec{a} = \hat{i} - \hat{j}$ , $\vec{b} = \hat{i} + \hat{j}$	(I)	$\frac{2}{\sqrt{5}}$
(B)	$\vec{a} = \hat{i} + \hat{j}$ , $\vec{b} = 2\hat{i} - \hat{k}$	(II)	0
(C)	$\vec{a} = \hat{j} + \hat{k}$ , $\vec{b} = \hat{i} + \hat{k}$	(III)	$\sqrt{2}$
(D)	$\vec{a} = 2\hat{i} + 3\hat{j}$ , $\vec{b} = \hat{i} - \hat{k}$	(IV)	$\frac{1}{\sqrt{2}}$

Choose the correct answer from the options given below :