CUET · MATHS · PYQ PAPER 2025
Which of the following statements are true?
(A) The vector joining the points P(2, 3, 0) Q(- 1, - 2, - 4) directed from P to Q is \(\overrightarrow{P Q}\) = - 3i - 5j - 4k
(B) Projection of a vector vec a on other vector \(\vec{b}\) is \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|}\)
(C) If \(\vec{a}=i-2 j+k\) and \(\vec{b}=-2 i+4 j+5 k\) then \(\vec{a}+\vec{b}=-i+2 j+6 k\)
(D) If \(\theta\) is the angle between \(\vec{a}\) and \(\vec{b}\) \(\cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}\)
Choose the correct answer from the options given below:
- A (A), (C) and (D) only
- B (A), (B) and (C) only
- C (B), (C) and (D) only
- D (C), (B) and (D) only
Answer & Solution
Correct Answer
(A) (A), (C) and (D) only
Step-by-step Solution
Detailed explanation
\(\overrightarrow{P Q} = (-1-2)i + (-2-3)j + (-4-0)k = -3i - 5j - 4k\) Statement (A) is true. Projection of \(\vec{a}\) on \(\vec{b}\) is \(\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}\). Statement (B) is false. \(\vec{a}+\vec{b} = (1-2)i + (-2+4)j + (1+5)k = -i + 2j + 6k\) Statement…
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