Mathematics - Vector Question with Solution | TestHub

(I) Let $(\vec{a}\times \vec{b})\times \vec{c}=-5\vec{a}+4\vec{b}$ and $\vec{a}\cdot \vec{b}=3$ and $\overrightarrow{\mathrm{a}}\times (\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{c}})=\lambda \overrightarrow{\mathrm{b}}+\mu \overrightarrow{\mathrm{c}}$, then $|\lambda |+|\mu |$ is (Where $\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{c}}$ are pairwise non-collinear)

(P) 2

(II) If sum of digits of the total No. of squares in chess board is given by k , then the value of ( $\mathrm{k}-1$ ) is

(Q) 7

(III) The line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies on the plane $2\mathrm{x}-4\mathrm{y}+\mathrm{z}=9$, then k is

(R) 9

(IV) Value of ${\int }_{-\pi /4}^{\pi /4}\frac{x^9-3x^7+x^5+1}{{\cos }^{2}x}dx$ is equal to

(S) 5

(T) 8