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  • Provide Solution for RD Sharma Class 12 Chapter 27 Straight Line in Space Exercise Fill in the blanks Question 7

Provide Solution for RD Sharma Class 12 Chapter 27 Straight Line in Space Exercise Fill in the blanks Question 7

Answers (1)

Answer :   0^{\circ}

Hint :   Use vector dot product

Given :  a, b, c \text { and } \frac{1}{b c}, \frac{1}{c a}, \frac{1}{a b}

Solution :  Let \overrightarrow{m 1} and \overrightarrow{m 2} be vectors parallel to the two given lines.

                 \therefore \overrightarrow{m 1}=a \hat{i}+b \hat{j}+c \hat{k}

                 And\; \overrightarrow{m 2}=\frac{1}{b c} i+\frac{1}{c a} j+\frac{1}{a b} \hat{k}

                 Let θ be angle between given lines

                 \therefore \theta \text { is angle between } \overrightarrow{m 1} \text { and } \overrightarrow{m 2}

                \therefore \cos \theta=\frac{\overrightarrow{m 1} \cdot \overrightarrow m 2}{|\overrightarrow{m 1}||\overrightarrow{m 2}|} =\frac{a\left(\frac{1}{b c}\right)+b\left(\frac{1}{c a}\right)+c\left(\frac{1}{a b}\right)}{\sqrt{a^{2}+b^{2}+c^{2}} \sqrt{\left(\frac{1}{b c}\right)^{2}+\left(\frac{1}{c a}\right)^{2}+\left(\frac{1}{a b}\right)^{2}}}=1

                \therefore \theta=0^{\circ}

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