Show that the points A, B, C with position vectors 2a ⃗+3b ⃗+5c ⃗, a ⃗+2b ⃗+3c ⃗ and 7a ⃗-c ⃗.......

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If a ⃗=i ̂+j ̂+k ̂ and b ⃗=j ̂-k ̂, find a vector c ⃗, such that a ⃗×c ⃗=b ⃗ and a ⃗⋅ c ⃗=3. If a ⃗=i ̂+j ̂+k ̂ and b ⃗=j ̂-k ̂, find a vector c ⃗, such that a ⃗×c ⃗=b ⃗ and a ⃗⋅ c ⃗=3.
If a ⃗=i ̂-j ̂+7k ̂ and b ⃗=5i ̂-j ̂+λk ̂, then find the value of λ, so that a ⃗+b ⃗ ........Q171 If a ⃗=i ̂-j ̂+7k ̂ and b ⃗=5i ̂-j ̂+λk ̂, then find the value of λ, so that a ⃗+b ⃗ ........Q171
If a ⃗ and b ⃗ are the position vectors of A and B respectively, find the position vector of a...... If a ⃗ and b ⃗ are the position vectors of A and B respectively, find the position vector of a......
Show that the points A(-2i ̂+3j ̂+5k ̂ ),B(i ̂+2j ̂+3k ̂ ) and C(7i ̂-k ̂ ) are collinear. ......Q86 Show that the points A(-2i ̂+3j ̂+5k ̂ ),B(i ̂+2j ̂+3k ̂ ) and C(7i ̂-k ̂ ) are collinear. ......Q86
Find (a ⃗+3b ⃗ ).(2a ⃗-b ⃗ ), if a ⃗=i ̂+j ̂+2k ̂ and b ⃗=3i ̂+2j ̂-k ̂ ........Q154 Find (a ⃗+3b ⃗ ).(2a ⃗-b ⃗ ), if a ⃗=i ̂+j ̂+2k ̂ and b ⃗=3i ̂+2j ̂-k ̂ ........Q154
The position vectors of points A, B and C are λi ̂+3j ̂,12i ̂+μj ̂ and 11i ̂-3j ̂ respectively..Q146 The position vectors of points A, B and C are λi ̂+3j ̂,12i ̂+μj ̂ and 11i ̂-3j ̂ respectively..Q146
If a ⃗, b ⃗, c ⃗ are three non-null vectors such that any two of them are non-collinear. If.... If a ⃗, b ⃗, c ⃗ are three non-null vectors such that any two of them are non-collinear. If....
Let a ⃗=i ̂+2j ̂-3k ̂ and b ⃗=3i ̂-j ̂+2k ̂ be two vectors. Show that the vectors (a ⃗+b ⃗ )....Q170 Let a ⃗=i ̂+2j ̂-3k ̂ and b ⃗=3i ̂-j ̂+2k ̂ be two vectors. Show that the vectors (a ⃗+b ⃗ )....Q170