Mathematics in Physics

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Question 1 of 121

A vector has magnitude same as that of A⃗=3j^+4j^\vec{A}=3\hat{j}+4\hat{j} and is parallel to B⃗=4i^+3j^\vec{B}=4\hat{i}+3\hat{j}. The xx and yy components of this vector in first quadrant are xx and 33 respectively where x=x=____.

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Answer: 4

Magnitude of vector ∣A⃗∣=32+42=5\left|\vec{A}\right|=\sqrt{{3}^{2}+{4}^{2}}=5
Now, unit vector along B⃗=(4i^+3j^)42+32=45i^+35j^\vec{B}=\dfrac{(4\hat{i}+3\hat{j})}{\sqrt{{4}^{2}+{3}^{2}}}=\dfrac{4}{5}\hat{i}+\dfrac{3}{5}\hat{j}
Now, N⃗=∣A⃗∣B^=5×(45i^+35j^)=4i^+3j^\vec{N}=\left|\vec{A}\right|\hat{B}=5\times \left(\dfrac{4}{5}\hat{i}+\dfrac{3}{5}\hat{j}\right)=4\hat{i}+3\hat{j}
∴x=4∴x=4

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