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MATHS Fill In The Blanks[1 Marks ]

Vector Algebra · Rajasthan Board (RBSE) STD 12 Science (Rajasthan - English Medium). 11 questions.

Questions

Fill In The Blanks[1 Marks ]

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11 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
If the angle between two non-zero vectors $\vec{a}$ and $\vec{b}$ is $\theta$, then $\cos \theta=$ ___________ .
Answer
$\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}$
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Question 31 Mark
If $\vec{a}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{b}=3 \hat{i}+5 \hat{j}-2 \hat{k}$, then the value of $|\vec{a} \times \vec{b}|$ will be ___________ .
Answer
$\sqrt{507}$
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Question 51 Mark
If $\vec{a}$ and $\vec{b}$ are two non-zero vactors and $\vec{a} \times \vec{b}=0$ if and only if $\vec{a}$ and $\vec{b}$ are. ___________ .
Answer
parallel to each other
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Question 61 Mark
If $\vec{a}$ is a unit vector and $(\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=15$, then the value of $|\vec{x}|$ will be __________ .
Answer
4
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Question 81 Mark
Suppose that $\vec{a}$ and $\vec{b}$ are two non-zero vectors. Then $\vec{a} \cdot \vec{b}=0$ if and only if ____________ .
Answer
$\vec{a}$ and $\vec{b}$ are mutually perpendicular.
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Question 91 Mark
Direction cosines of vector $\vec{a}=\hat{i}+\hat{j}-2 \hat{k}$ will be ___________ .
Answer
$\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}$
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Question 101 Mark
Two vectors $\vec{a}$ and $\vec{b}$ are called equal vectors if their ___________ .
Answer
magnitudes and directions are the same.
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Question 111 Mark
The numbers $l r, m r$ and $n r$ proportional to direction cosines are called __________ of $\vec{r}$.
Answer
direction ratios
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Fill In The Blanks[1 Marks ] - MATHS STD 12 Science Questions - Vidyadip