Angle and Magnitude of Unit Vector
Vector Algebra

87917 If \(|a+b|=a-b \mid\), then \(a\) and \(b\) are

1 parallel
2 perpendicular
3 angle between a and \(\mathrm{b}\) is \(45^{\circ}\)
4 angle between \(\mathrm{a}\) and \(\mathrm{b}\) is \(60^{\circ}\)
Vector Algebra

87952 The image of the point with position vector \(\hat{\mathbf{i}}+3 \hat{k}\) in the plane \(r .(\hat{i}+\hat{j}+\hat{k})=1\) is

1 \(\hat{i}+2 \hat{j}+\hat{k}\)
2 \(\hat{i}-2 \hat{j}+\hat{k}\)
3 \(-\hat{i}-2 \hat{j}+\hat{k}\)
4 \(\hat{i}+2 \hat{j}-\hat{k}\)
Vector Algebra

87926 The measure of the angle between the line \(\overrightarrow{\mathbf{r}}=(2,-3,1)+\mathbf{k}(2,2,1) ; k \in: R\) and the plane \(2 \mathrm{x}\) \(-2 y+z+7=0\) is

1 \(\tan ^{-1} \frac{1}{4 \sqrt{5}}\)
2 \(\sin ^{-1} \frac{1}{3}\)
3 \(\cos ^{-1} \frac{1}{9}\)
4 \(\pi / 2\)
Vector Algebra

87901 The value of \(x\) if \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector is

1 \(\pm \frac{1}{\sqrt{3}}\)
2 \(\pm \sqrt{3}\)
3 \(\pm 3\)
4 \(\pm \frac{1}{3}\)
Vector Algebra

87902 If \(\vec{p}=x \vec{a}+y \vec{b}+z \vec{c}\) and \(\vec{p}=3 \hat{i}+2 \hat{j}+4 \hat{k}\),
where \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{c}}=\hat{\mathbf{k}}+\hat{\mathbf{i}}\), then value of \(\mathbf{x}, \mathbf{y}, \mathrm{z}\) are respectively

1 \(\frac{3}{2}, \frac{1}{2}, \frac{5}{2}\)
2 \(\frac{5}{2}, \frac{3}{2}, \frac{1}{2}\)
3 \(\frac{1}{2}, \frac{3}{2}, \frac{-5}{2}\)
4 \(\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\)
Vector Algebra

87917 If \(|a+b|=a-b \mid\), then \(a\) and \(b\) are

1 parallel
2 perpendicular
3 angle between a and \(\mathrm{b}\) is \(45^{\circ}\)
4 angle between \(\mathrm{a}\) and \(\mathrm{b}\) is \(60^{\circ}\)
Vector Algebra

87952 The image of the point with position vector \(\hat{\mathbf{i}}+3 \hat{k}\) in the plane \(r .(\hat{i}+\hat{j}+\hat{k})=1\) is

1 \(\hat{i}+2 \hat{j}+\hat{k}\)
2 \(\hat{i}-2 \hat{j}+\hat{k}\)
3 \(-\hat{i}-2 \hat{j}+\hat{k}\)
4 \(\hat{i}+2 \hat{j}-\hat{k}\)
Vector Algebra

87926 The measure of the angle between the line \(\overrightarrow{\mathbf{r}}=(2,-3,1)+\mathbf{k}(2,2,1) ; k \in: R\) and the plane \(2 \mathrm{x}\) \(-2 y+z+7=0\) is

1 \(\tan ^{-1} \frac{1}{4 \sqrt{5}}\)
2 \(\sin ^{-1} \frac{1}{3}\)
3 \(\cos ^{-1} \frac{1}{9}\)
4 \(\pi / 2\)
Vector Algebra

87901 The value of \(x\) if \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector is

1 \(\pm \frac{1}{\sqrt{3}}\)
2 \(\pm \sqrt{3}\)
3 \(\pm 3\)
4 \(\pm \frac{1}{3}\)
Vector Algebra

87902 If \(\vec{p}=x \vec{a}+y \vec{b}+z \vec{c}\) and \(\vec{p}=3 \hat{i}+2 \hat{j}+4 \hat{k}\),
where \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{c}}=\hat{\mathbf{k}}+\hat{\mathbf{i}}\), then value of \(\mathbf{x}, \mathbf{y}, \mathrm{z}\) are respectively

1 \(\frac{3}{2}, \frac{1}{2}, \frac{5}{2}\)
2 \(\frac{5}{2}, \frac{3}{2}, \frac{1}{2}\)
3 \(\frac{1}{2}, \frac{3}{2}, \frac{-5}{2}\)
4 \(\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\)
Vector Algebra

87917 If \(|a+b|=a-b \mid\), then \(a\) and \(b\) are

1 parallel
2 perpendicular
3 angle between a and \(\mathrm{b}\) is \(45^{\circ}\)
4 angle between \(\mathrm{a}\) and \(\mathrm{b}\) is \(60^{\circ}\)
Vector Algebra

87952 The image of the point with position vector \(\hat{\mathbf{i}}+3 \hat{k}\) in the plane \(r .(\hat{i}+\hat{j}+\hat{k})=1\) is

1 \(\hat{i}+2 \hat{j}+\hat{k}\)
2 \(\hat{i}-2 \hat{j}+\hat{k}\)
3 \(-\hat{i}-2 \hat{j}+\hat{k}\)
4 \(\hat{i}+2 \hat{j}-\hat{k}\)
Vector Algebra

87926 The measure of the angle between the line \(\overrightarrow{\mathbf{r}}=(2,-3,1)+\mathbf{k}(2,2,1) ; k \in: R\) and the plane \(2 \mathrm{x}\) \(-2 y+z+7=0\) is

1 \(\tan ^{-1} \frac{1}{4 \sqrt{5}}\)
2 \(\sin ^{-1} \frac{1}{3}\)
3 \(\cos ^{-1} \frac{1}{9}\)
4 \(\pi / 2\)
Vector Algebra

87901 The value of \(x\) if \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector is

1 \(\pm \frac{1}{\sqrt{3}}\)
2 \(\pm \sqrt{3}\)
3 \(\pm 3\)
4 \(\pm \frac{1}{3}\)
Vector Algebra

87902 If \(\vec{p}=x \vec{a}+y \vec{b}+z \vec{c}\) and \(\vec{p}=3 \hat{i}+2 \hat{j}+4 \hat{k}\),
where \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{c}}=\hat{\mathbf{k}}+\hat{\mathbf{i}}\), then value of \(\mathbf{x}, \mathbf{y}, \mathrm{z}\) are respectively

1 \(\frac{3}{2}, \frac{1}{2}, \frac{5}{2}\)
2 \(\frac{5}{2}, \frac{3}{2}, \frac{1}{2}\)
3 \(\frac{1}{2}, \frac{3}{2}, \frac{-5}{2}\)
4 \(\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\)
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Vector Algebra

87917 If \(|a+b|=a-b \mid\), then \(a\) and \(b\) are

1 parallel
2 perpendicular
3 angle between a and \(\mathrm{b}\) is \(45^{\circ}\)
4 angle between \(\mathrm{a}\) and \(\mathrm{b}\) is \(60^{\circ}\)
Vector Algebra

87952 The image of the point with position vector \(\hat{\mathbf{i}}+3 \hat{k}\) in the plane \(r .(\hat{i}+\hat{j}+\hat{k})=1\) is

1 \(\hat{i}+2 \hat{j}+\hat{k}\)
2 \(\hat{i}-2 \hat{j}+\hat{k}\)
3 \(-\hat{i}-2 \hat{j}+\hat{k}\)
4 \(\hat{i}+2 \hat{j}-\hat{k}\)
Vector Algebra

87926 The measure of the angle between the line \(\overrightarrow{\mathbf{r}}=(2,-3,1)+\mathbf{k}(2,2,1) ; k \in: R\) and the plane \(2 \mathrm{x}\) \(-2 y+z+7=0\) is

1 \(\tan ^{-1} \frac{1}{4 \sqrt{5}}\)
2 \(\sin ^{-1} \frac{1}{3}\)
3 \(\cos ^{-1} \frac{1}{9}\)
4 \(\pi / 2\)
Vector Algebra

87901 The value of \(x\) if \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector is

1 \(\pm \frac{1}{\sqrt{3}}\)
2 \(\pm \sqrt{3}\)
3 \(\pm 3\)
4 \(\pm \frac{1}{3}\)
Vector Algebra

87902 If \(\vec{p}=x \vec{a}+y \vec{b}+z \vec{c}\) and \(\vec{p}=3 \hat{i}+2 \hat{j}+4 \hat{k}\),
where \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{c}}=\hat{\mathbf{k}}+\hat{\mathbf{i}}\), then value of \(\mathbf{x}, \mathbf{y}, \mathrm{z}\) are respectively

1 \(\frac{3}{2}, \frac{1}{2}, \frac{5}{2}\)
2 \(\frac{5}{2}, \frac{3}{2}, \frac{1}{2}\)
3 \(\frac{1}{2}, \frac{3}{2}, \frac{-5}{2}\)
4 \(\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\)
Vector Algebra

87917 If \(|a+b|=a-b \mid\), then \(a\) and \(b\) are

1 parallel
2 perpendicular
3 angle between a and \(\mathrm{b}\) is \(45^{\circ}\)
4 angle between \(\mathrm{a}\) and \(\mathrm{b}\) is \(60^{\circ}\)
Vector Algebra

87952 The image of the point with position vector \(\hat{\mathbf{i}}+3 \hat{k}\) in the plane \(r .(\hat{i}+\hat{j}+\hat{k})=1\) is

1 \(\hat{i}+2 \hat{j}+\hat{k}\)
2 \(\hat{i}-2 \hat{j}+\hat{k}\)
3 \(-\hat{i}-2 \hat{j}+\hat{k}\)
4 \(\hat{i}+2 \hat{j}-\hat{k}\)
Vector Algebra

87926 The measure of the angle between the line \(\overrightarrow{\mathbf{r}}=(2,-3,1)+\mathbf{k}(2,2,1) ; k \in: R\) and the plane \(2 \mathrm{x}\) \(-2 y+z+7=0\) is

1 \(\tan ^{-1} \frac{1}{4 \sqrt{5}}\)
2 \(\sin ^{-1} \frac{1}{3}\)
3 \(\cos ^{-1} \frac{1}{9}\)
4 \(\pi / 2\)
Vector Algebra

87901 The value of \(x\) if \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector is

1 \(\pm \frac{1}{\sqrt{3}}\)
2 \(\pm \sqrt{3}\)
3 \(\pm 3\)
4 \(\pm \frac{1}{3}\)
Vector Algebra

87902 If \(\vec{p}=x \vec{a}+y \vec{b}+z \vec{c}\) and \(\vec{p}=3 \hat{i}+2 \hat{j}+4 \hat{k}\),
where \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{c}}=\hat{\mathbf{k}}+\hat{\mathbf{i}}\), then value of \(\mathbf{x}, \mathbf{y}, \mathrm{z}\) are respectively

1 \(\frac{3}{2}, \frac{1}{2}, \frac{5}{2}\)
2 \(\frac{5}{2}, \frac{3}{2}, \frac{1}{2}\)
3 \(\frac{1}{2}, \frac{3}{2}, \frac{-5}{2}\)
4 \(\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\)