Test Index

CBSE Class 12 Math 2013 Solved Paper

© examsnet.com
Question : 8 of 29
Marks: +1, -0
a unit vector a⃗\vec{a} makes angle π3\frac{\pi}{3} with i^,π4\hat{i}, \frac{\pi}{4} with j^\hat{j} and acute angle θ with k^\hat{k} , then find the value of θ.
Solution:  
Let a⃗\vec{a} = xi^+yj^+zk^x\hat{i}+y\hat{j}+z\hat{k} be the unit vector.
∴ x = cos π3\frac{\pi}{3} = 12\frac{1}{2}
y = cos π4\frac{\pi}{4} = 12\frac{1}{\sqrt{2}}
Now, x2+y2+z2x^2+y^2+z^2 = 1
⇒ (12)2+(12)2+z2\left(\frac{1}{2}\right)^2+\left(\frac{1}{\sqrt{2}}\right)^2+z^2 = 1
⇒ z2z^2 = 1 - 14−12\frac{1}{4}-\frac{1}{2} = 14\frac{1}{4}
⇒ z = 12\frac{1}{2}
∴ cos θ = 12\frac{1}{2} ⇒ θ = π3\frac{\pi}{3}
© examsnet.com
Go to Question:
Prev Question
Next Question