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[mathjax] Question 1 (i) यदि (If) A=[2 3 5] तथा (and) $B=\begin{bmatrix}1\\2\\3\end{bmatrix}$ , find AB निकालें Sol : (ii) यदि (if) A=$\begin{bmatrix}2&1&3\\4&1&0\end{bmatrix}$ तथा...
[mathjax] Question 2 आव्यूह को संभव कांटियाँ क्या हैं यदि इसमे (i) 5 अवयव हैं (ii) 8 अवयव हैं (iii) 24 अवयव हैं (iv) 13 अवयव हैं (v) 18 अवयव हैं [What are the possible orders a matrix can have if it...
[mathjax] TYPE 1 Question 1 Find the value of (i) $sin^{-1} \left(\dfrac{\sqrt{3}}{2}\right)$ Sol : Let $sin^{-1} \left(\dfrac{\sqrt{3}}{2}\right)= \theta$..(i) ⇒$sin \theta =\dfrac{\sqrt{3}}{2}$...
[mathjax] Question 1 Find the cartesian equations of the following planes whose vector equations are (i) $\vec{r} \cdot(3 \hat{i}+3 \hat{j}-4 \hat{k})=0$ (ii) $\vec{r} \cdot(2 \hat{i}-7 \hat{j}+4...
[mathjax] Question 1 If the lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\quad \frac{x-1}{3 k}=\frac{y-1}{1}=\frac{z-6}{-5}$ are perpendicular, Find the value of k. Sol : Question 2 Show...
[mathjax] Question 1 [निम्नलिखित प्रत्येक रेखा युग्म के बीच का कोण ज्ञात करें] Find the angle between each of the following pair of lines : (i) $\vec{r}=5 \hat{i}-7 \hat{j}+\lambda(-\hat{i}+4...
[mathjax] Question 1 (i) यदि एक रेखा x, y तथा z-अक्षों की धनात्मक दिशा के साथ क्रमश $90^{\circ}, 60^{\circ}, 30^{\circ}$ का कोण बनाती है तो इसकी दिक्-कोसाइन ज्ञात कीजिए । [If a line makes angles...
[mathjax] Question 1 दिखाएँ कि तीन बिन्दुएँ जिनके स्थिति सदिश $-3 \hat{i}+\hat{j}+5 \hat{k}, 2 \hat{i}+3 \hat{k},-13 \hat{i}+3 \hat{j}+9 \hat{k}$ हैं, संरेख हैं। Sol : माना तीन बिन्दुओं के स्थिति...
[mathjax] यदि दो सदिश $\vec{a}$ और $\vec{b}$ इस प्रकार हैं कि $|\vec{a}|=2,|\vec{b}|=7$ तथा $\vec{a} \times \vec{b}=3 \hat{i}+2 \hat{j}+6 \hat{k}$ तों $\vec{a}$ और $\vec{b}$ के बीच का कोण ज्ञात करे।...
[mathjax] Question 1 सदिश $\vec{a}$ तथा $\vec{b}$ का अदिश गुणनफल ज्ञात करें, जहाँ [Find the scalar product of vectors $\vec{a}$ and $\vec{b}$, where] (i) $\hat{a}=2 \hat{\imath}+4 \hat{k}, \hat{b}=3...
[mathjax] Question 1 दिखाएँ कि निम्नलिखित तीन बिन्दुएँ संरेख है। [Prove that the following three points are collinear] (i) $-2 \vec{a}+3 \vec{b}+5 \vec{c}, \vec{a}+2 \vec{b}+3 \vec{c}, 7...
[mathjax] Question 1 चार बिन्दुओ A,B,C,D के स्थिति सदिश क्रमशः $\vec{a}, \vec{b}, 2 \vec{a}+3 \vec{b}$ तथा $\vec{a}-2 \vec{b}$ है। सदिश $\overrightarrow{\mathrm{AC}}, \overrightarrow{\mathrm{DB}},...