CUET · MATHS · PYQ PAPER 2025
If \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is:
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\vec{a}+\vec{b}=-\vec{c}\) \(|\vec{a}+\vec{b}|^2=|-\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2\vec{a}\cdot\vec{b}=|\vec{c}|^2\) \(3^2+5^2+2(3)(5)\cos\theta=7^2\) \(9+25+30\cos\theta=49\) \(34+30\cos\theta=49\) \(30\cos\theta=15\) \(\cos\theta=\frac{1}{2}\) \(\theta=\frac{\pi}{3}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is :CUET 2025 Medium
- A small company manufactures necklaces and bracelets. The combined number of necklaces and bracelets it can handle per day is at the most 24 .A bracelet takes 1 hour to make and a necklace takes half hour to be made.Maximum number of hours available per day is 16 .If the number of necklaces and bracelets made per day is \(x\) and \(y\)
respectively then the time constraint for the L.P.P.is :CUET 2023 Hard - If \(A=\left|\begin{array}{ccc}x & -3 & 4 \\ 3 & y & -5 \\ -4 & z & 0\end{array}\right|\) is a Skew-Symmetric matrix and \(a d j A=\left[a_{i j}\right]_{3 \times 3}\), then \(a_{11}+a_{22}+a_{33}\) is equal to:CUET 2025 Hard
- A tub contains \(60\) litres of milk. From this tub, \(6\) litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?CUET 2025 Hard
- \(\frac{d}{d x}\left(e^{2 \log _e x^3}\right)\) equalsCUET 2025 Hard
- If \(A = [a_{ij}]\) be a square matrix of order n, then the correct statements are:
A. A is a symmetric matrix if and only if \(A^T = A\).
B. A is a skew-symmetric matrix if and only if \(A^T = -A\).
C. If order of A is n x n, then order of \(A^T\) is m \(\times\) n (m\(\neq\)n).
D. If \(\begin{bmatrix} 1 & 2 \\ 3 & 2x \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 3 & 2x \end{bmatrix}\) then x = 4.
Choose the correct answer from the options given below.CUET 2023 Hard
More PYQs from CUET
- Which one of the following plants is the source of cannabinoids commonly used in drug abuse?CUET 2023 Medium
- The rise and fall of share market is an example ofCUET 2025 Hard
- Select the correct relation of half life for a zero order reaction.CUET 2025 Hard
- Given below are some stages of human evolution. Arrange them in correct sequence (Past to Recent)
(A) Homo habilis
(B) Homo sapiens
(C) Homo neanderthalensis
(D) Homo erectus
Choose the correct answer from the options given below:CUET 2023 Hard - Calculated value of magnetic moment (BM) of an aqueous solution of \(M n ^{ 2 + }\) is ___________CUET 2025 Easy
- The angle between the line \(\frac{x+2}{3}=\frac{y-3}{2}=\frac{z+5}{6}\) and the plane 2x + 10y - 11z = 5 is:CUET 2023 Easy