CBSE 12th Standard Maths Subject Vector Algebra Ncert Exemplar 4 Mark Questions With Solution 2021
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CBSE 12th Standard Maths Subject Vector Algebra Ncert Exemplar 4 Mark Questions With Solution 2021
12th Standard CBSE
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Reg.No. :
Maths
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If \(\overrightarrow { a } =\hat { i } -\hat { j } +7\hat { k } \) and \(\overrightarrow { b } =5\hat { i } -\hat { j } +\lambda \hat { k } \) then find the value of \(\lambda\) so that the vectors \(\overrightarrow { a } +\overrightarrow { b } \ and\ \overrightarrow { a } -\overrightarrow { b } \) are orthogonal.
(a) -
If \(\overrightarrow { a } \times \overrightarrow { b } =\overrightarrow { a } \times \overrightarrow { c } \ and\ \overrightarrow { a } \times \overrightarrow { c } =\overrightarrow { b } \times \overrightarrow { d } \) prove that \(\overrightarrow { a } -\overrightarrow { d } \) is parallel to \(\overrightarrow { b } -\overrightarrow { c } \) provided \(\overrightarrow { a } \neq \overrightarrow { d } \ and\ \overrightarrow { b } \neq \overrightarrow { c } \)
(a) -
It is given that:\(\overset { \rightarrow }{ x } =\frac { \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ y } \frac { \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } and\ \overset { \rightarrow }{ z } =\frac { \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } \) where \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are non-coplanar vectors.
(a) -
If a vector \(\vec{r}\) has magnitude 14and direction ratios 2, 3 and - 6. Then, find the direction cosines and components of \(\vec{r}\)given that \(\vec{r}\) makes an acute angle with x-axis.
(a) -
If the three vectors \(\vec{a}, \vec{b} \text { and } \vec{c}\) are given as \(a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}, b_{1} \hat{i}+b_{2} \hat{j}+b_{3} \hat{k} \text { and } c_{1} \hat{i}+c_{2} \hat{j}+c_{3} \hat{k}\) Then, show that \(\vec{a} \times(\vec{b}+\vec{c})=(\vec{a} \times \vec{b})+(\vec{a} \times \vec{c})\).
(a)
4 Marks
