CUET Mathematics - Let OA = 2i - j + k and OB = i + j - k. Then A. The magnitude of vector OA is 6 B. The magnitude of vector OB is sqrt(3) C. The vector AB is (-i + 2j - 2k) D. OA * OB = 0 E. OA OB Choose the correct answer from the options given below: | PYQs + Solutions

22 May Shift 2

let $\vec{a}$ be a non-zero vector of magnitude ' $a$ ' and $\lambda$ is a non-zero scalar, then $\lambda\vec{a}$ is a unit vector if

30 Aug Shift 1

If $\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are two non zero vectors inclined at an angle $\theta$ , then identify the correct option out of the given options.

(a) $\cos\theta = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot |\vec{b}|}$

(b) $\vec{a}$ and $\vec{b}$ are perpendicular, if $a_1 b_1 + a_2 b_2 + a_3 b_3 = 0$

(c) $\vec{a}$ and $\vec{b}$ are perpendicular, if $\frac{a_1}{b_1} = \frac{a_2}{b_2} \neq \frac{c_1}{c_2}$

(d) for $\theta = \pi$ , $\vec{a} \times \vec{b} = 0$

(e) $\cos\theta = \frac{|\vec{a} \times \vec{b}|}{|\vec{a}| \cdot |\vec{b}|}$

Choose the most appropriate answer from the options given below

21 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The vectors $\lambda\hat{i}$ $+ \hat{j} + 2\hat{k}$ and $\vec{i} + \lambda\hat{j} + \hat{k}$ are perpendicular if λ is equal to	(I) 1
(B) The vectors $3\hat{i} + 6\hat{j} - \hat{k}$ and $2\hat{i} + 4\hat{j} - \lambda\hat{k}$ are collinear if λ is equal to	(II) -1
(C) The number of vectors of unit-length which are perpendicular to both the vectors $\vec{a}$ = $\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b}$ = $3\hat{i} - \hat{j} + 5\hat{k}$ is	(III) 2/3
(D) If $\lvert \vec{a} \rvert = 1$ and $\vec{a} + \vec{b} = \vec{0}$ , then $\lvert \vec{b} \rvert$ is equal to	(IV) 2

Choose the correct answer from the options given below:

CUET Mathematics 2022 6 Aug Shift 2 PYQs

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