87866
If \(\vec{a}\) and \(\vec{b}\) are unit vectors then what is the angle between \(\vec{a}\) and \(\vec{b}\) for \(\sqrt{3} \vec{a}-\vec{b}\) to be unit vector?
87867
Suppose \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7\), then the angle between \(\vec{a} \& \vec{b}\) is
1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Explanation:
(C) : Given, \(\vec{a}+\vec{b}+\vec{c}=0, \quad|\vec{a}|=3,|\vec{b}|=5\) \(|\vec{c}|=7\) \(\vec{a}+\vec{b}+\vec{c}=0\) \(\vec{a}+\vec{b}=-\vec{c}\) \(|\vec{a}+\vec{b}|^2=|-\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2 \vec{a} \vec{b}=|\vec{c}|^2\) \((3)^2+(5)^2+2|\vec{a}||\vec{b}| \cos \theta=|7|^2\) \(9+25+2(3 \times 5) \cos \theta=49\) \(30 \cos \theta=15\) \(\cos \theta=\frac{15}{30}\) \(\cos \theta=\frac{1}{2}=\cos \frac{\pi}{3}\) \(\theta=\frac{\pi}{3}\) The angle between \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is \(\frac{\pi}{3}\).
Karnataka CET-2016
Vector Algebra
87868
A space vector makes the angles \(150^{\circ}\) and \(60^{\circ}\) with the positive direction of \(X\) and \(Y\) axes. The angle made by the vector with the positive direction of \(\mathrm{Z}\)-axis is
87869
If \(\mathbf{p}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{q}}=4 \hat{\mathbf{k}}-\hat{\mathbf{j}}\) and \(\overrightarrow{\mathbf{r}}=\hat{\mathbf{i}}+\hat{\mathbf{k}}\) then the and unit vector in the direction of \(3 \vec{p}+\vec{q}-2 \vec{r}\) is
87866
If \(\vec{a}\) and \(\vec{b}\) are unit vectors then what is the angle between \(\vec{a}\) and \(\vec{b}\) for \(\sqrt{3} \vec{a}-\vec{b}\) to be unit vector?
87867
Suppose \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7\), then the angle between \(\vec{a} \& \vec{b}\) is
1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Explanation:
(C) : Given, \(\vec{a}+\vec{b}+\vec{c}=0, \quad|\vec{a}|=3,|\vec{b}|=5\) \(|\vec{c}|=7\) \(\vec{a}+\vec{b}+\vec{c}=0\) \(\vec{a}+\vec{b}=-\vec{c}\) \(|\vec{a}+\vec{b}|^2=|-\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2 \vec{a} \vec{b}=|\vec{c}|^2\) \((3)^2+(5)^2+2|\vec{a}||\vec{b}| \cos \theta=|7|^2\) \(9+25+2(3 \times 5) \cos \theta=49\) \(30 \cos \theta=15\) \(\cos \theta=\frac{15}{30}\) \(\cos \theta=\frac{1}{2}=\cos \frac{\pi}{3}\) \(\theta=\frac{\pi}{3}\) The angle between \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is \(\frac{\pi}{3}\).
Karnataka CET-2016
Vector Algebra
87868
A space vector makes the angles \(150^{\circ}\) and \(60^{\circ}\) with the positive direction of \(X\) and \(Y\) axes. The angle made by the vector with the positive direction of \(\mathrm{Z}\)-axis is
87869
If \(\mathbf{p}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{q}}=4 \hat{\mathbf{k}}-\hat{\mathbf{j}}\) and \(\overrightarrow{\mathbf{r}}=\hat{\mathbf{i}}+\hat{\mathbf{k}}\) then the and unit vector in the direction of \(3 \vec{p}+\vec{q}-2 \vec{r}\) is
87866
If \(\vec{a}\) and \(\vec{b}\) are unit vectors then what is the angle between \(\vec{a}\) and \(\vec{b}\) for \(\sqrt{3} \vec{a}-\vec{b}\) to be unit vector?
87867
Suppose \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7\), then the angle between \(\vec{a} \& \vec{b}\) is
1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Explanation:
(C) : Given, \(\vec{a}+\vec{b}+\vec{c}=0, \quad|\vec{a}|=3,|\vec{b}|=5\) \(|\vec{c}|=7\) \(\vec{a}+\vec{b}+\vec{c}=0\) \(\vec{a}+\vec{b}=-\vec{c}\) \(|\vec{a}+\vec{b}|^2=|-\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2 \vec{a} \vec{b}=|\vec{c}|^2\) \((3)^2+(5)^2+2|\vec{a}||\vec{b}| \cos \theta=|7|^2\) \(9+25+2(3 \times 5) \cos \theta=49\) \(30 \cos \theta=15\) \(\cos \theta=\frac{15}{30}\) \(\cos \theta=\frac{1}{2}=\cos \frac{\pi}{3}\) \(\theta=\frac{\pi}{3}\) The angle between \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is \(\frac{\pi}{3}\).
Karnataka CET-2016
Vector Algebra
87868
A space vector makes the angles \(150^{\circ}\) and \(60^{\circ}\) with the positive direction of \(X\) and \(Y\) axes. The angle made by the vector with the positive direction of \(\mathrm{Z}\)-axis is
87869
If \(\mathbf{p}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{q}}=4 \hat{\mathbf{k}}-\hat{\mathbf{j}}\) and \(\overrightarrow{\mathbf{r}}=\hat{\mathbf{i}}+\hat{\mathbf{k}}\) then the and unit vector in the direction of \(3 \vec{p}+\vec{q}-2 \vec{r}\) is
87866
If \(\vec{a}\) and \(\vec{b}\) are unit vectors then what is the angle between \(\vec{a}\) and \(\vec{b}\) for \(\sqrt{3} \vec{a}-\vec{b}\) to be unit vector?
87867
Suppose \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=5,|\vec{c}|=7\), then the angle between \(\vec{a} \& \vec{b}\) is
1 \(\pi\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{4}\)
Explanation:
(C) : Given, \(\vec{a}+\vec{b}+\vec{c}=0, \quad|\vec{a}|=3,|\vec{b}|=5\) \(|\vec{c}|=7\) \(\vec{a}+\vec{b}+\vec{c}=0\) \(\vec{a}+\vec{b}=-\vec{c}\) \(|\vec{a}+\vec{b}|^2=|-\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2 \vec{a} \vec{b}=|\vec{c}|^2\) \((3)^2+(5)^2+2|\vec{a}||\vec{b}| \cos \theta=|7|^2\) \(9+25+2(3 \times 5) \cos \theta=49\) \(30 \cos \theta=15\) \(\cos \theta=\frac{15}{30}\) \(\cos \theta=\frac{1}{2}=\cos \frac{\pi}{3}\) \(\theta=\frac{\pi}{3}\) The angle between \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is \(\frac{\pi}{3}\).
Karnataka CET-2016
Vector Algebra
87868
A space vector makes the angles \(150^{\circ}\) and \(60^{\circ}\) with the positive direction of \(X\) and \(Y\) axes. The angle made by the vector with the positive direction of \(\mathrm{Z}\)-axis is
87869
If \(\mathbf{p}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{q}}=4 \hat{\mathbf{k}}-\hat{\mathbf{j}}\) and \(\overrightarrow{\mathbf{r}}=\hat{\mathbf{i}}+\hat{\mathbf{k}}\) then the and unit vector in the direction of \(3 \vec{p}+\vec{q}-2 \vec{r}\) is
