Question

Find the vector that must be added to the vector Î - 3^j 3+ 2k^ and
3 ^i + 6^j - 7^k so that the
resultant vector is a unit vector along y-axis.
a) - 4 î - 2^j + 5^k
b) - 4 î + 2^j + 5^k
C) 4 Î- 2 ^j + 5^k
d) -4Î - 2 ^j- ^k
​

Answer 1

ANSWER :

• Option c) $\sf -4 \hat{i} \: - \: 2 \hat{j} \: + \: 5 \hat{k}$

GIVEN :

• $\sf \hat{i} \: - 3 \hat{j} \: + 2 \hat{k}$
• $\sf 3 \hat{i} \: + 6 \hat{j} \: - 7 \hat{k}$

TO FIND :

• The vector that must be added to the given vector so that the resultant vector is a unit vector along y - axis.

SOLUTION :

$\implies \sf A + B + C \: = \: j$

Here,

→ J is the unit vector.

→ C is the resultant vector.

$\implies \sf B - A \: = \: (\hat{i} \: - 3 \hat{j} \: + \: 2 \hat{k}) \: - \: (\hat{i} \: + \: 6 \hat{j} \: - 7 \hat{k})$

$\implies \sf A + B \: = \: 4 \hat{i} \: + \: 3 \hat{j} \: - \: 5 \hat{k}$

$\sf Now, \: Using \: subst \: rule,$

$\implies \sf 4 \hat{i} \: + \: 3 \hat{j} \: + \: c \: = \: j$

$\implies \sf c \: = \: j \: - \: (4 \hat{i} \: + \: 3 \hat{j} \: - \: 5 \hat{k})$

$\implies \sf j \: = \: 4 \hat{i} \: - \: 3 \hat{j} \: + \: 5 \hat{k}$

$\implies \sf -4 \hat{i} \: - \: 2 \hat{j} \: + \: 5 \hat{k}$

$\therefore \sf -4 \hat{i} \: - \: 2 \hat{j} \: + \: 5 \hat{k}$