Question

If a=i+j+k ,b= 4i-2j+3k and c=i-2j+k find a vector of magnitude 6 units which is parallel to the vector 2a-b+3c

Answer 1

Answer:

$2(\hat i - 2 \hat j + 2\hat k)$

Step-by-step explanation:

If a=i+j+k ,b= 4i-2j+3k and c=i-2j+k .

find a vector of magnitude 6 units which is parallel to the vector 2a-b+3c=r

vector parallel to

$\vec r=2 \vec a - \vec b + 3\vec c \\ \\ = 2( \hat i + \hat j + \hat k) - ( 4\hat i - 2 \hat j +3 \hat k) + 3( \hat i - 2 \hat j + \hat k) \\ \\ = 2 \hat i + 2\hat j +2 \hat k -4 \hat i + 2\hat j - 3 \hat k + 3\hat i - 6 \hat j +3 \hat k \\ \\ \vec r = \hat i - 2 \hat j + 2\hat k$

Unit vector in direction of parallel vector

$= \frac{ \vec r}{ |\vec r| } \\ \\ = \frac{ \hat i - 2 \hat j + 2\hat k}{ \sqrt{1 + 4 + 4} } \\ \\ = \frac{1}{3} (\hat i - 2 \hat j + 2\hat k)$

Vector parallel to given vectors having magnitude 6

$=6 \times \frac{1}{3}( \hat i - 2 \hat j + 2\hat k) \\ \\ = 2(\hat i - 2 \hat j + 2\hat k) \\\\or\\ \\=2\hat i - 4 \hat j + 4\hat k$

Hope it helps you.