Two adjacent sides of a parallelogram ABCD are given by $\overrightarrow { \mathrm { AB } } = 2 \hat { \mathrm { i } } + 10 \hat { \mathrm { j } } + 11 \hat { \mathrm { k } }$ and $\overrightarrow { \mathrm { AD } } = - \hat { \mathrm { i } } + 2 \hat { \mathrm { j } } + 2 \hat { \mathrm { k } }$ The side AD is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that AD becomes $\mathrm { AD } ^ { \prime }$. If $\mathrm { AD } ^ { \prime }$ makes a right angle with the side AB , then the cosine of the angle $\alpha$ is given by A) $\frac { 8 } { 9 }$ B) $\frac { \sqrt { 17 } } { 9 }$ C) $\frac { 1 } { 9 }$ D) $\frac { 4 \sqrt { 5 } } { 9 }$
Two adjacent sides of a parallelogram ABCD are given by $\overrightarrow { \mathrm { AB } } = 2 \hat { \mathrm { i } } + 10 \hat { \mathrm { j } } + 11 \hat { \mathrm { k } }$ and $\overrightarrow { \mathrm { AD } } = - \hat { \mathrm { i } } + 2 \hat { \mathrm { j } } + 2 \hat { \mathrm { k } }$
The side AD is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that AD becomes $\mathrm { AD } ^ { \prime }$. If $\mathrm { AD } ^ { \prime }$ makes a right angle with the side AB , then the cosine of the angle $\alpha$ is given by\\
A) $\frac { 8 } { 9 }$\\
B) $\frac { \sqrt { 17 } } { 9 }$\\
C) $\frac { 1 } { 9 }$\\
D) $\frac { 4 \sqrt { 5 } } { 9 }$