JEE Advance - Mathematics (2001 - No. 3)
Find $$3-$$dimensional vectors $${\overrightarrow v _1},{\overrightarrow v _2},{\overrightarrow v _3}$$ satisfying
$$\,{\overrightarrow v _1}.{\overrightarrow v _1} = 4,\,{\overrightarrow v _1}.{\overrightarrow v _2} = - 2,\,{\overrightarrow v _1}.{\overrightarrow v _3} = 6,\,\,{\overrightarrow v _2}.{\overrightarrow v _2}$$
$$ = 2,\,{\overrightarrow v _2}.{\overrightarrow v _3} = - 5,\,{\overrightarrow v _3}.{\overrightarrow v _3} = 29$$
$$\,{\overrightarrow v _1}.{\overrightarrow v _1} = 4,\,{\overrightarrow v _1}.{\overrightarrow v _2} = - 2,\,{\overrightarrow v _1}.{\overrightarrow v _3} = 6,\,\,{\overrightarrow v _2}.{\overrightarrow v _2}$$
$$ = 2,\,{\overrightarrow v _2}.{\overrightarrow v _3} = - 5,\,{\overrightarrow v _3}.{\overrightarrow v _3} = 29$$
$$\,{\overrightarrow v _1} = 2\widehat i\,\,\,\,{\overrightarrow v _2} = - \widehat i + \widehat j\,\,\,\,{\overrightarrow v _3} = 3\widehat i + 2\widehat j + 4\widehat k$$
$$\,{\overrightarrow v _1} = 2\widehat i\,\,\,\,{\overrightarrow v _2} = - \widehat i - \widehat j\,\,\,\,{\overrightarrow v _3} = 3\widehat i - 2\widehat j - 4\widehat k$$
$$\,{\overrightarrow v _1} = 2\widehat i\,\,\,\,{\overrightarrow v _2} = - \widehat i + \widehat j\,\,\,\,{\overrightarrow v _3} = 3\widehat i + 2\widehat j - 4\widehat k$$
$$\,{\overrightarrow v _1} = 2\widehat i\,\,\,\,{\overrightarrow v _2} = - \widehat i - \widehat j\,\,\,\,{\overrightarrow v _3} = 3\widehat i + 2\widehat j + 4\widehat k$$
$$\,{\overrightarrow v _1} = 2\widehat i\,\,\,\,{\overrightarrow v _2} = - \widehat i + \widehat j\,\,\,\,{\overrightarrow v _3} = 3\widehat i + 2\widehat j + 4\widehat k$$
Comments (0)
